near-inertial current variability off the east coast of...

理學博士學位論文

Near-inertial Current Variability

off the East Coast of Korea

韓國東海沿岸準慣性週期海流變動性

2006 年 8 月

서울大學校大學院

地球環境科學部

南成賢


off the East Coast of Korea 韓國東海沿岸準慣性週期海流變動性

指導敎授金坵

이 論文을 理學博士學位論文으로 提出함

2006 年 8 月

서울大學校大學院

地球環境科學部

南成賢

南成賢 의 理學博士學位論文으로 認准함

2006 年 8 月

委員長 (印)

副委員長 (印)

委員 (印)

委員 (印)

委員 (印)


off the East Coast of Korea

A

Ph.D. Dissertation

by

SungHyun NAM

Supervisor: Prof. Kuh KIM

Thesis Committee:

Im-Sang OH Committee Chairman

Seoul National University

Sang-Ho LEE Kyung-Il CHANG Kunsan National University Seoul National University

Young-Gyu PARK Kuh KIM Korea Ocean Research and Seoul National University

Development Institute

August 2006

i

Publication list

Refereed Articles (2004-2006): 1. Kim, H. R., S. H. Nam, D. J. Kim, K. Kim, and W. M. Moon, Reply to comment by Q. Zheng

on “Can near-inertial internal waves in the East Sea be observed by synthetic aperture radar?” Geophysical Research Letters 32(20), L02607, doi:10.1029/2005GL024351, 2005.

2. Hahm, D. S., G. Kim, S. H. Nam, Y. W. Lee, K.-R. Kim, and K. Kim, Tidal influence on the sea-to-air transfer of CH4 in the coastal ocean, Tellus-B, 57, 1-7, 2005.

3. Nam, S. H., G. Kim, K.-R. Kim, K. Kim, L. Oh, K.-W. Kim, H. Ossi, Application of real-time monitoring buoy systems for physical and biogeochemical parameters in the coastal ocean around the Korean peninsula, Marine Technology Society Journal, 39(2), 54-64, 2005.

4. Nam, S. H., Y. H. Kim, K.-A. Park, and K. Kim, Spatio-temporal variability in sea surface wind stress near and off the east coast of Korea, Acta Oceanologica Sinica, 24(1), 107-114, 2005.

5. Kim, D-. J., S. H. Nam, H.-R. Kim, K. Kim, and W. M. Moon, Can near-inertial internal waves in the East Sea be observed by synthetic aperture radar? Geophysical Research Letters 32(2) L02606, doi:10.1029/2004GL021532, 2005.

6. Kim, K., Y. B. Kim, J. J. Park, S. H. Nam, K. -A. Park, and K. -I. Chang, Long-term and real-time monitoring system of the East/Japan Sea, Ocean Science Journal 40(1) 25-44, 2005.

7. Nam, S. H., J.-Y. Yun, and K. Kim, Observations on the coastal ocean response to Typhoon Maemi at the East Sea Real-time Ocean Buoy, Journal of the Korean Society of Oceanography (Bada)- Special issue, 9 (3), 111-118, 2004. (in Korean)

8. Nam, S. H., S. J. Lyu, Y. H. Kim, K. Kim, J-.H. Park, D. R. Watts, Correction on TOPEX/POSEIDON altimeter data for nonisostatic sea level response to atmospheric pressure in the Japan/East Sea, Geophysical Research Letters 31(2), L02304, 10.1029/2003GL018487, 2004.

Conference Abstracts (2003-2006): 1. Nam, S. H., K.-I. Chang, and K. Kim, Local change of depth-integrated near-inertial

kinetic energy off the east coast of Korea, In Proceedings of the spring meeting of Korean Society of Oceanography in Busan, Korea, 2006.

2. Nam, S. H., H. R. Kim, D.-J. Kim, Y.-G. Kim, and K. Kim, Spatio-temporal characteristics of highly nonlinear internal waves in the East (Japan) Sea, In Proceedings of the AGU 2006 Ocean Science Meeting in Honolulu, Hawaii, US, 2006.

3. Nam, S. H., H. R. Kim, D.-J. Kim, Y.-G. Kim, and K. Kim, Spatio-temporal characteristics of

nonlinear internal solitary waves in the East Sea, In Proceedings of the Korean Acoustical Society in Jinhae, Korea, 2005.

4. Kim, H. R., S. H. Nam, Y. G. Kim, and K. Kim, Numerical modeling of internal soliton shoaling, In Proceedings of the Korean Acoustical Society in Jinhae, Korea, 2005.

5. Nam, S. H., and K. Kim, Near-inertial internal waves and subinertial motions observed near the mid-east coast of Korea, In Proceedings of Dynamic Planet 2005 in Cairns, Australia, 2005.

6. Nam, S. H., K.-W. Kim, H. Ossi, G. Kim, K.-R. Kim, and K. Kim, Real-time monitoring of physical and biogeochemical parameters using an ocean buoy system: Applied to the coastal ocean around the Korean peninsula, In Proceedings of 13th PAMS/JECSS in Bali, Indonesia, 2005.

7. Nam, S. H., and K. Kim, Nonlinear interaction between near-inertial internal waves and subinertial motions observed near the steeply-sloping bottom at the mid-east coast of Korea, In Proceedings of the spring meeting of Korean Society of Oceanography in Busan, Korea, 2005.

8. Nam, S. H., S. J. Lyu, and K. Kim, Correction of altimetry data for nonisostatic sea level response to atmospheric pressure in the East (Japan) Sea, In Proceedings of the International Geoscience And Remote Sensing Symposium (IGARSS) 2005 in Seoul, Korea, 2005. (invited)

9. Nam, S. H., K.-W. Kim, and K. Kim, Real-time ocean monitoring buoy and coastal ocean variability, In Proceedings of the Asia and Pacific Coast (APAC) 2005 in Jeju Island, Korea, 2005.

10. Nam, S. H., S. J. Lyu, Y. H. Kim, and K. Kim, Correction of multiple-mission satellite altimetry data for non-isostatic sea level response to atmospheric pressure in the

ii

East Sea and their merging, In Proceedings of the spring meeting of Korean Society of Oceanography in Busan, Korea, 2005.

11. Kim, K., Y.-B. Kim, J.-J. Park, S. H. Nam, K.-A. Park, and K.-I. Chang, Long-term and real-time monitoring system of the East/Japan Sea, In Proceedings of the international workshop on the East Sea Circulation in Pusan, Korea, 2004.

12. Han, B. W., S. H. Nam, J.-Y. Yun, K. Kim, S.-I. Kim, and Y.-G.. Kim, Physical characteristics of internal waves and its influence on acoustic propagation in the East Sea, Proceedings of 19th meeting of the Acoustical Society of Korea in Pyoung-chang, Korea, 2004.

13. Nam, S. H., J. J. Park, Y. B. Kim, K.-A. Park, J.-Y. Yun, D.-J. Kim, W.-M. Moon, and K. Kim,

Observing systems in the East (Japan) Sea: a monitoring buoy with moored instruments, surface and subsurface drifting floats, and satellite measurements, Proceedings of the North Pacific Marine Science Organization (PICES) 13rd annual meeting in Honolulu, Hawaii, U.S., 2004.

14. Kim, K., S. H. Nam, D.-J. Kim, K.-W. Kim, H. Ossi, Y.-G. Kim, and J.-W. Seo, Real-time wave measurement using an ocean monitoring buoy, In Proceedings of the workshop on wave, tide observations and modelings in the Asian-Pacific region (ACECC-TC1 Workshop) in Seoul, Korea, 2004.

15. Kim, D.-J., W. M. Moon, S. H. Nam, and K. Kim, Investigation of internal waves in the

East (Japan) Sea using synthetic aperture radar, In Proceedings of ENVISAT Symposium in Salzburg, Austria, 2004.

16. Nam, S. H., Y. H. Kim, J. J. Park, Y. B. Kim, J.-Y. Yun, and K. Kim, Characteristics of monthly mean current near the mid-east coast of Korea, In Proceedings of the spring meeting of Korean Society of Oceanography in Pusan, Korea, 2004.

17. Nam, S. H., D.-J. Kim, J.-Y. Yun, W. M. Moon, and K. Kim, Coastal ocean response to the passage of the typhoon ‘MAEMI’ across the East (Japan) Sea, In Proceedings of 1st Asia-Oceania Geoscience Society (AOGS) meeting in Singapore, Singapore, 2004.

18. Nam, S. H., H. R. Kim, J.-Y. Yun, and K. Kim, Deformation of internal solitary waves observed near the mid-east coast of Korea, In Proceedings of 1st Asia-Oceania Geoscience Society (AOGS) meeting in Singapore, Singapore, 2004.

19. Nam, S. H, B. W. Han, Y. H. Kim, J.-Y. Yun, K. Kim, S.-I. Kim, and Y. G. Kim, Characteristics of internal waves and their impact on acoustic transmission near the east coast of Korea, In Proceedings of Maritime Weapon System Workshop in Jainhae, Korea, 2004.

20. Nam, S. H., K. W. Kim, J. J. Park, Y. H. Kim, J. Y. Yun, and K. Kim, Observation on the abrupt ocean changes during the typhoon ‘MAEMI’ period in the East Sea, In Proceedings of the fall meeting of Korean Society of Oceanography in Ansan, Korea, 2003.

21. Nam, S. H., K. A. Park, and K. Kim, Spatio-temporal variability in sea surface wind-stress off the Korean east coast, In Proceedings of 12th PAMS/JECSS in Hangzhu, China, 2003.

22. Nam, S. H., S. J. Lyu, and K. Kim, Correction of high-frequency (2-20 days) fluctuation effects on the TOPEX/POSEIDON altimeter data in the East (Japan) Sea, Proceedings of the North Pacific Marine Science Organization (PICES) 13rd annual meeting in Seoul, Korea, 2003. (Best Paper Award in POC)

23. Kim, Y. H., S. H. Nam, S. J. Lyu, K. Kim, Y. G. Kim, and T. B. Shim, 2002-2003 observation on the short-period internal waves near and off the Donghae city, Korea, 18th Underwater Acoustics Symposium In Proceedings, Korea, 2003.

24. Kim, D. J., W. M. Moon, S. H. Nam, Evaluation of ENVISAT ASAR data for measurement of surface wind field over the Korean east coast, In Proceedings of the International Geoscience And Remote Sensing Symposium (IGARSS) 2003 in Toulouse, France, 2003.

25. Nam, S. H., S. J. Lyu, and K. Kim, Local sea level response to atmospheric pressure and Kelvin wave propagation along the coast around the Korean peninsula, In Proceedings of International Union of Geodesy and Geophysics (IUGG) 2003 in Sapporo, Japan, 2003.

26. Nam, S. H., H. R. Kim, Y. H. Kim, S. J. Lyu, S. W. Park, J. Y. Yun, and K. Kim, Wintertime, short-period internal waves in the coastal region near Donghae city, Korea, In Proceedings of the spring meeting of Korean Society of Oceanography in Jeju Island, Korea, 2003.

27. Nam, S. H., Y. B. Kim, Y. H. Kim, S. J. Lyu, B. Y. Han, J. Y. Yun, and K. Kim, Propagation and reflection of near-inertial and semi-diurnal internal waves off the Korean east coast, In Proceedings of the spring meeting of Korean Society of Oceanography in Jeju Island, Korea, 2003.

28. Nam, S. H., Y. H. Kim, S. J. Lyu, J. J. Park, K. W. Kim, H. Ossi, and K. Kim, Development of ESROB (East Sea Real-time Ocean Buoy) off the Korean east coast, In Proceedings of ADCPs (Acoustic Doppler Current Profilers) in Action in San Diego, California, US, 2003.

(invited)

iii

Abstract

Near-inertial (NI) oscillations are described by analysis of Eulerian currents

measured in the coastal region off the east coast of Korea in 1999-2004, and the

mechanics associated with the NI oscillations are elucidated. Wind-induced mixed layer

(ML) inertial motions that are accounted for by linear damped slab model, trapping and

expelling of NI waves under upwelling and downwelling conditions, and upward

propagation of NI wave energy due to forward bottom reflection, explain 53%, 30%,

and 17% of the NI oscillations observed in the coastal region. In particular, schematics

of three-dimensional ray paths of NI energy radiations are suggested for the upwelling,

downwelling and transition conditions in the steep sloped coastal region with local

evaluation on the horizontal and vertical directions of NI waves. Depth-integrated,

subsurface NI kinetic energy (KE) in the region are primarily changed by both local and

remote sources of energy exchange that are local wind work flux and the horizontal flux

due to radiating NI waves. At the interior of water column in the region, horizontal

convergence of NI KE occurs in upwelling periods whereas divergence in downwelling

periods. Intermittent ML inertial motions driven by local wind disturbance, subinertial

variations of background coastal jet (or coastal front associated with current shear), and

different type of bottom reflection mainly depending on horizontal direction of NI

waves are proposed to be responsible for the intermittent and heterogeneous

characteristics of NI oscillations with temporal scales of a few days to week and

horizontal (vertical) scales of few km (few to few tens of m). Such intermittent and

heterogeneous NI oscillations have significance on intermittently localized enhancement

of turbulent mixing in the coastal region, particularly when the wave-wave interactions,

i.e. between the NI waves and semi-diurnal internal tides, are considered.

Keywords: Near-inertial oscillations, Near-inertial waves, Near-inertial kinetic energy,

Subinertial current shear, Coastal upwelling and downwelling, Steeply sloping bottom,

Propagation and reflection of near-inertial waves, off the east coast of Korea

Student Number: 2001-31230

iv

Contents

Publication list i

Abstract iii

Contents iv

List of Figures viii

List of Tables xiv

Chapter I. Introduction

1. Background and motivation 1

a. Near-inertial waves under background shear in a stratified coastal ocean 1

b. Coastal region off the east coast of Korea 6

2. Purpose 9

3. Outline 12

Chapter II. Field Measurements and Data

1. Real-time ocean monitoring buoy 14

2. Field experiments 17

3. Data processing 18

Chapter III. Characteristics of Near-inertial Variability off the East

Coast of Korea

1. Vertical and temporal variations 22

2. Complex empirical orthogonal function (CEOF) analysis 24

3. Horizontal ellipse 26

a. Polarization 26

b. Ellipticity 28

4. Kinetic energy 28

a. Vertical and temporal variations 28

b. KE EOF 31

c. Depth-integrated near-inertial kinetic energy 34

5. Crossshore structure (May 2002) 37

a. Spatial and temporal variations 37

v

b. Sectional KE EOF 39

Chapter IV. Wind-induced, Local Generations of Mixed Layer Near-

inertial Oscillations

1. Local wind variability 43

a. Buoy wind stress 43

b. Subinertial buoy wind stress and spatially-averaged ECMWF wind stress 45

c. Super-inertial wind stress variability 48

d. EOF of ECMWF wind stress 48

2. Mixed layer variability 50

a. Estimation of mixed layer depth and mixed layer density 50

b. Temporal variations of mixed layer depth and mixed layer density 52

3. Application of a linear damped slab model 52

4. Comparison of modeled and observed near-inertial kinetic energy 55

5. Possible sources for the discrepancy 57

a. Non-uniform, super-inertial wind stress variability 57

b. Near-inertial wave propagation, coastal boundary effect, and background current

57

Chapter V. Propagation and reflection of near-inertial waves

1. Background conditions 59

a. Upwelling/downwelling favorable wind conditions 59

b. Sectional structure of density, geostrophic current and horizontal shear 61

2. Three-dimensional directions of near-inertial waves 63

a. Horizontal direction of near-inertial wave propagation 64

b. Vertical tilt angle of near-inertial waves 64

3. Roles of subinertial shear on the behavior of near-inertial waves 69

a. Change in vertical tilt angle of near-inertial waves 69

b. Trapping/expelling of near-inertial waves 70

4. Roles of sloping bottom on the behavior of near-inertial waves 71

5. Ray path of near-inertial waves 76

vi

a. Upwelling case (August 2001, July 2002, October 2003, and May 2004) 76

b. Downwelling case (May, August, and November 2003) 78

c. Transition case 80

d. Summary 82

Chapter VI. Source for Local Change of Depth-integrated Near-

inertial Kinetic Energy

1. Local change of depth-integrated, subsurface near-inertial kinetic energy

84

2. Local and remote sources of subsurface near-inertial kinetic energy 85

a. Local budget of near-inertial kinetic energy 85

b. Main causes of local, subsurface near-inertial kinetic energy change 87

3. Horizontal energy flux 88

Chapter VII. Discussions

1. Comparison with near-inertial oscillations in other shelf regions 93

a. Inner New Jersey shelf (observations) 93

b. New England shelf and Texas-Louisiana shelf (observations) 94

c. Oregon continental shelf (model results) 96

2. Unexplained characteristics of near-inertial oscillations in the region 97

a. Rectilinear near-inertial oscillations in the surface mixed layer 97

b. Discontinuous phase propagation 98

3. Significance of near-inertial oscillations on coastal ocean mixing 99

a. Semi-diurnal internal tides and wave-wave interaction 99

b. Intermittently localized turbulent mixing enhancement 101

Chapter VIII. Summaries, Conclusion and Suggestions

1. Summaries and conclusion 102

2. Underlying questions and suggestions for future study 108

vii

References 111

Abstract (in Korean) 118

Appendices

I. Derivation of dispersion relation for near-inertial waves under background

subinertial motions 119

II. Filling ADCP data gap caused by vertical migration of zooplankton 123

Funded programs 125

Acknowledgements 126

Curriculum Vitae 129

viii

List of Figures

Figure I-1. Schematic diagrams for evolution of near-inertial wave energy in the coastal

region under the intermittent wind work at surface, density stratification, and

steep bottom slope (a) without and (b) with subinertial motions that accompany

nearshore coastal front and associated current shear. 3

Figure I-2. Previous theoretical/numerical model studies and observational studies

about the effects of coastal boundary, and the combined effects of sloping

bottom and background (subinertial) current shear (or nearshore coastal front) on

the near-inertial wave behavior in the coastal region. 7

Figure I-3. Location and bottom topography in the study area. Here, the coastal area of

intensive observations which corresponds to the domain of Figure II-1 are

marked as a small box in left map and a dashed box in right map. The large box

in left map coincides to the domain of right map. The contours in right map are

depths in meter. 10

Figure II-1. Positions of Eulerian measurements (N2, S1, S2, and S3), CTD stations (1-

14) with bottom topography (in meter) in the coastal area of extensive

observations marked in Figure I-3. The water depths at S1, N2, S2, and S3 are

20, 100, 130, and 190 m, respectively. The ESROB, PKNUB, TRBM and

ESOREC denote the East Sea Real-time Ocean Buoy, Pu-Kyung National

University Buoy, and the East Sea Ocean REsearch Center (37oN 35’). The

photo of instruments and sectional view of the measurements are shown in right

panel. 15

Figure II-2. Crossshore currents measured at 55, 65, 70, and 75 m of S3 before (black)

and after (blue) vertical interpolation. The data gap at 65, 70, and 75 m in night

can cause over-smoothing of near-inertial currents when they are band-pass

filtered. 19

Figure II-3. Auto-spectra of crossshore currents measured at 50 m of S2 in 2003 (thick

black), 80 m of S2 in 2003 (thin black), and 80 m of N2 in 2001 (gray) and filter

response function for low-pass (gray) and band-pass (black) filters used in the

study. The criteria of subinertial and near-inertial frequencies that are 30 hours

and near 19 hours (17-20 hours) respectively are noted as vertical gray lines.

21

Figure III-1. Time-depth contours of near-inertial currents in the alongshore (v) and

crossshore (u) directions where the time units are days from January 1, 1999.

Total 40 events are indicated as bracketed numbers when and where the NI

currents are significantly (> 3 cm/s) enhanced. 23

Figure III-2. Vertical profiles of first four modes (A1, A2, A3, and A4) complex

empirical orthogonal functions (CEOFs) accounting for 80% of total variance

ix

indicate that the magnitudes of near-inertial currents generally decrease with

depth. The current vectors of 1st and 2nd modes CEOFs (56%) rotate clockwise

whereas those of 3rd and 4th modes CEOFs (24%) counterclockwise with depth,

indicative of downward and upward propagations of near-inertial energy,

respectively. 25

Figure III-3. Time coefficients of first four modes (B1, B2, B3, and B4) complex

empirical orthogonal functions (CEOFs) where those of 1st and 2nd modes

CEOFs and 3rd and 4th modes CEOFs are shown in the left and right panels,

respectively. Intermittent modulations of the time coefficients during the events

are separated as periods of B1 and B2 dominant or those of B3 and B4 dominant.

27

Figure III-4. Time-depth contours of the polarization of near-inertial current ellipse in

the horizontal plane that is defined as an angle of major axis orientation from the

east in degrees. The events are separated as those when the polarization is close

to crossshore direction (red) and alongshore direction (blue). Here, the

polarization is shown when and where the near-inertial currents exceed 3 cm/s.

29

Figure III-5. Same as Figure III-4 but the ellipticity of near-inertial current ellipse that

is defined as a ratio of minor axis to major axis from zero to unity. Similarly, the

events are separated as those when the ellipticity is close to zero (rectilinear, red)

and unity (circular, blue). 30

Figure III-6. Time-depth contours of near-inertial kinetic energy per unit mass (cm2/s

2),

where the 40 events are marked as bracketed numbers. Though the kinetic

energy is enhanced at the upper levels during many events, there are the events

when the kinetic energy is significant in the interior as denoted with boxed

numbers. 32

Figure III-7. Vertical structures of first four modes EOFs (E1, E2, E3, and E4) of near-

inertial kinetic energy, which account for 80% of total variance. First mode EOF

of which the most variances are confined at the upper levels explains only 45%

and the three other modes EOFs (35%) have the structure of significant interior

variations of kinetic energy. 33

Figure III-8. Time coefficients of first four modes (F1, F2, F3, and F4) EOFs of near-

inertial kinetic energy where the peaks during the events (numbered) are

separated as those when the 1 mode EOF is dominant and those when the 2-4

modes are comparable (boxed numbers). 35

Figure III-9. Time series of depth-integrated near-inertial kinetic energy per unit are in

J/m2, where 40 events are marked as bracketed numbers. Particularly large (80

J/m2) depth-integrated kinetic energy is observed in the region during the events

denoted as shaded numbers. Temporal structure of such events do not show clear

seasonal pattern. 36

x

Figure III-10. Time-depth contours of crossshore (upper left) and alongshore (upper

right) near-inertial currents and the kinetic energy (down right) observed at S1,

S2, and S3 for Days 1216-1228 (from April 30 to May 12, 2002) where the

vertical lines separate the periods of 2-4 days named Leg-I, II, III (corresponding

to the event (13)), and IV (events (14)). 38

Figure III-11. Schematic sectional view of crossshore structure of near-inertial energy

(up left), first three sectional EOFs (G1, G2, and G3,) of near-inertial kinetic

energy (accounting for 81% of total variance during the Leg-I, II, III, and IV)

(down), and the associate time coefficients (H1, H2, and H3,) (up right) where the

Leg-I, II, III, and IV are divided. 42

Figure IV-1. Time series of alongshore (black) and crossshore (gray) wind stresses

from 1999 to 2004, measured at N2 (1999-2001) and S2 (2002-2004). 44

Figure IV-2. Time series of low-pass (with half power centered at 30 hours) filtered,

alongshore (black) and crossshore (gray) wind stresses and the spatially-

averaged (over the 4 by 4 degrees area noted as blue shaded area in left map)

alongshore (blue) and crossshore (baby blue) ECMWF wind stresses. Here, the

pink and sky blue shaded boxes indicate the upwelling and downwelling

favorable wind conditions and the vertical arrows with the pink and sky blue

colors are the time of CTD measurements displaying upwelling and

downwelling sectional structures, respectively. 46

Figure IV-3. Time series of the low-pass filtered buoy wind stress minus the spatially-

averaged ECMWF wind stress in the alongshore (red) and crossshore (pink)

directions, respectively. Here, the periods are marked when the non-uniformity

of wind stress distributions is significant. 47

Figure IV-4. Time series of high-pass (half power centered at 30 hours) alongshore

(red) and crossshore (pink) wind stresses where the periods of strong high-

frequency wind stress fluctuations are in well agreement with those of

significant non-uniformity of wind stress in the region. 49

Figure IV-5. (a) Spatial distributions of first two EOFs of ECMWF wind stresses which

account for the most (93%) of total variance, (b) associate time coefficients from

1999 to 2001, and (c) auto-spectra of the time coefficients [Nam et al., 2005b].

Here, during the periods of non-uniform and strong high-frequency wind stress

fluctuations (denoted in (b)), the time coefficients of 2nd EOF are in negative

phases. 51

Figure IV-6. (a) Two examples of density profiles observed at N2 in 2000 with the

mixed layer depth and the mean density in the mixed layer. (b) Time series of

the mixed layer depth in meters and the mean density (sigma-t) in the mixed

layer. Seasonal pattern is clear in both time series, i.e. deep and shallow mixed

layers, and high and low densities in winter and summer, respectively. 53

xi

Figure IV-7. Time series of (full) depth-integrated near-inertial kinetic energy (red,

same as in Figure III-9), mixed layer integrated near-inertial kinetic energy

(gray), and the results of damped slab model where the near-inertial kinetic

energy are integrated from surface to mixed layer depth. The events when the

model over-estimates, under-estimates and is not able to reproduce the

observations are denoted as bracketed numbers. The events marked as green and

purple shades are the periods when the polarization is close to the crossshore

directions (and the ellipticity is mostly close to the recti-linear case) and when

the downward phase propagation (upward energy propagation) is dominant. The

events when the interior kinetic energy is significant are denoted with red boxes

in the event numbers. 56

Figure V-1. Distribution of ECMWF wind stress averaged over the periods (a) from

July 5-16, 2002 (Days 1283-1294), and (b) from May 1-12, 2003 (Days 1582-

1593). Here, the upwelling favorable and downwelling favorable wind

conditions in the study region (marked as circle point) are clearly shown in (a)

and (b), respectively. 60

Figure V-2. Distribution of ECMWF wind stress (up) averaged over the periods (a)

from March 30-April 9, 2000 and (b) May 17-27, 1999, indicative of upwelling

favorable and downwelling favorable wind conditions, respectively. The cross-

sectional structures of alongshore geostrophic currents (middle), density in

sigma-t (down, lines), and associate horizontal shear of alongshore currents

(down, color scale) during those periods are shown. 62

Figure V-3. Schematic diagrams for the particle motions of inertio-gravity waves with

phase (C) and group (Cg) velocities in (a) three-dimensional view, (b) horizontal

view, and (c) sectional view [Gill, 1982; Kundu, 1990]. 65

Figure V-4. Vertical tilt angles (theta) of near-inertial waves, tan-1

(k/m)+ (left) and tan-

1(k/m) (right) for waves of frequency feff+0.1f (up) and feff+0.3f (down) as a

function of vertical shear of (alongshore) subinertial current (Vz) and squared

buoyancy frequency (N2), where the contours are in degrees from the horizontal.

The angles during ten events (each are denoted as different symbol) when the

propagation and reflection of near-inertial waves are important in accounting for

the observed near-inertial oscillations are marked in the counters. The depth

levels where the angles are evaluated during the ten events are summarized in

Table V-1. 67

Figure V-5. Histograms of near-inertial kinetic energy averaged over the depth of 20-

100 m during all the (a) upwelling and (b) downwelling periods, where the

cumulative frequency of 95% is denoted. Statistically, the near-inertial kinetic

energies during upwelling periods are as double large as those during the

downwelling periods. Moreover, the highly enhanced (> 13 cm2/s

2) near-inertial

kinetic energy only occurred during the upwelling periods. 72

xii

Figure V-6. Schematic diagrams of bottom reflection of near-inertial waves for the case

of (a) backward reflection and (b) forward reflection. Here, C and Cg represent

the phase and group velocities, and suffix ‘i’ and ‘r’ represent incident and

reflected waves, respectively. When the horizontal direction of near-inertial

waves are close to the crossshore direction, the backward bottom reflection

would occur due to the steep (compare to the vertical tilt angles of near-inertial

waves) bottom slope in the direction. However, the forward bottom reflection is

much possible due to the gentle bottom slope when the horizontal direction of

near-inertial waves are almost parallel to the alongshore direction. 74

Figure V-7. Schematics of (a) horizontal structure of subinertial currents at the upper

(black) and lower (gray) depth levels, and (b) sectional and (c) horizontal views

of ray path of near-inertial wave energy under the upwelling conditions in

August 2001 (event (11)), July 2002 (event (16) and (17)), October 2003 (event

(29)), and May 2004 (event (36)). Here, the sign of horizontal shear or relative

vorticity is shown together in (a). The numbers in (b) are the vertical tilt angles

in x-z plane for the near-inertial waves of frequency feff+0.1f and the characters

‘R’ and ‘T’ in (b) represent the reflection and trapping of near-inertial waves in

the location, respectively. Black and gray arrows in (b) and (c) denote onshore

and offshore energy radiations, respectively. 77

Figure V-8. Same as Figure V-7 but the downwelling conditions in May (event (21)),

August (event (26)), and November 2003 (event (32)). The characters ‘E’ in (b)

represent the expelling of near-inertial waves in the location. 79

Figure V-9. Same as Figure V-7 but the transition (from downwelling ot upwelling)

conditions in May 2002 (event (13) and (14)). 81

Figure VI-1. Time series of local change of depth-integrated (from 20 to 100 m) near-

inertial kinetic energy (dashed gray), and the time rate of work done by local

wind (solid black) in W/m2 for (a) upwelling (events (11), (10), (17), (29), and

(36)), (b) transition (events (13) and (14)), (c) downwelling (events (21), (26),

and (32)), and (d) other cases. Durations of all the time series shown here are 10

days. 86

Figure VI-2. Schematic diagram for local and remote sources of local depth-integrated

near-inertial kinetic energy changes in the location of water column, which are

the local wind work flux and the horizontal energy flux primarily through the

radiation of near-inertial waves. 89

Figure VI-3. Time series of (a) local change of depth-integrated near-inertial kinetic

energy, (b) time rate of local wind work, (c) depth-integrated near-inertial

kinetic energy, and (d) the horizontal energy flux that is estimated from the

observations from Day 1200 to Day 1600. Here, positive (negative) values in (d)

represents the convergence (divergence) of near-inertial kinetic energy in the

region. Typical upwelling and downwelling periods in July 2002 and May 2003

are highlighted with pink and gray-sky blue colored rectangles. 91

xiii

Figure VII-1. Physical regimes of the study region off the east coast of Korea (gray

shaded), inner New Jersey shelf, New England shelf, Texas-Louisiana shelf, and

Oregon shelf in the domain where the x-axis is the distance from the coast

normalized to the internal radius of Rossby deformation and the y-axis is the

bottom slope. Since the study region has both steep bottom slope and proximity

to the coastal boundary, the bottom reflection of near-inertial waves and the

interaction between near-inertial waves and subinertial current shear associate

with coastal jet have an important role in subsurface near-inertial oscillations in

the region. 95

Figure VII-2. Auto-spectra of cross-shore currents measured at 50 m of S2 in 2003

(thick black), 80 m of S2 in 2003 (thin black), and 80 m of N2 in 2001 (gray),

same as shown in Figure II-3. Here, the periods of d2-f, d1, f, d2, d4-f, d2+f, d4,

and d6 correspond to 31, 24, 19.6, 12, 8.6, 7.4, 6, and 4 hours, respectively. In

spite of similar spectral densities at the tidal and tide-related interaction

frequencies (gray vertical lines, d1, d2, d4, and d6), those near the inertial and

the inertial-tidal interaction frequencies (back vertical lines, d2-f, f, d4-f, d2+f)

display significant difference among the spectra of the currents at different time

and different depths. 100

Figure A-II-1. Schematic views of buoy ADCP measurements with scatterers in day

and night times (up), and time-depth distribution of available (good quality)

ADCP data acquired at S3 (down), where blanks denote the data gap. The data

gap occurred below 60 m mostly for night times. 124

xiv

List of Tables

Table II-1. Periods, position, sampling interval, depth ranges or levels of ESROB (East

Sea Real-time Ocean Buoy) measurements. 16

Table III-1. Vertical directions of phase propagations of near-inertial currents during

Leg-I, II, III, and IV where the directions only for the cases of enhanced (3

cm2/s

2) near-inertial kinetic energy are shown. 40

Table V-1. Depth levels where the vertical tilt angle of near-inertial waves is evaluated

for the ten cases of events (11)-August 2001, (13) and (14)-May 2002, (16) and

(17)-July 2002, (21)-May 2003, (26)-August 2003, (29)-October 2003, (32)-

November 2003, and (36)-May 2004. 68

Table V-2. Polarization, vertical direction of near-inertial energy propagation, and the

type of bottom reflection for the ten cases in Table V-1. 75

Table VIII-1. Summary of primary mechanics accounting for the observed near-inertial

oscillations during the 40 events, where the MLIM, upwelling and downwelling,

and reflection denote the mixed layer inertial motion (23 events, 53%), the near-

inertial wave propagations under upwelling and downwelling conditions (13

events, 30%), and the forward and backward bottom reflection of near-inertial

waves (7 events, 17%), respectively. 103

1

Chapter I. Introduction

1. Background and motivation

a. Near-inertial oscillations under background shear in a stratified coastal ocean

Near-inertial (hereafter NI) oscillations are known to exist commonly within the

ocean. They are seen as clockwise (anticlockwise) rotating near-circular horizontal

currents in the northern (southern) hemisphere, with frequencies slightly higher than the

local inertial frequency. Many characteristics of wind-driven NI oscillations at the upper

ocean are relatively well understood [Gill, 1982; Pollard, 1980; Pollard, 1970; Pollard

and Millard, 1970]. Although these oscillations are most energetic in the mixed layer,

the energy can propagate downward into the deep ocean through the main thermocline.

Numbers of observational and numerical studies have examined this deep drainage of

NI energy [Park and Watts, 2005; Shcherbina et al., 2003; Lee and Niiler, 1998; van

Meurs, 1996; D’asaro, 1995; Levine and Zervakis, 1995] based on the nonlinear

interactions between the NI waves and background field, i.e. mesoscale eddies [Young

and Ben Jelloul, 1997; Kunze, 1985]. For example, the NI waves can be trapped in a

region of negative vorticity, i.e. inside the warm eddy in the northern hemisphere,

transferring NI energy in the deep ocean. However, the whole processes concerned with

the NI oscillations in the coastal ocean are still not always clear as different physical

conditions from the open ocean such as coastal boundary, sloping bottom and coastal jet

and front, complicate them.

2

Many theoretical and numerical model studies have investigated the roles of coastal

boundary, sloping bottom, and background (subinertial1) motions on NI wave behavior.

In a stratified coastal ocean, similarly to the case of open ocean [Park and Watts, 2005;

Shcherbina et al., 2003; Lee and Niiler, 1998; Kunze, 1985] the evolution of NI waves

is much constrained by the presence of nearshore front associated with background

current structure as demonstrated by recent numerical works [Davies and Xing, 2005;

Davies and Xing, 2003; Federiuk and Allen, 1996; Tintore et al., 1995; Xing and Davies,

2005; Xing et al., 2004; Xing and Davies, 2003] due to nonlinear interaction between

the NI waves and background current shears [Kunze, 1985]. With time-varying

nearshore coastal front (subinertial current shear), the evolution of NI waves becomes

more complex due to the interaction compared to the case without background current

shear (Figure I-1).

Including these nonlinear interactions associated with background (subinertial)

current shear, the dispersion relation of NI waves is expressed as (derived in Appendix

I)

m

k

z

V

m

k

f

Nf

eff ∂∂

−

+≈

22

2ω (Eqn. I-1)

where ω , N , f and eff

f are wave frequency, buoyancy frequency, Coriolis frequency

and the effective Coriolis frequency that can be approximated near the coastal boundary

as horizontal shear of alongshore current, i.e. x

Vffeff ∂

∂+=

2

1 [Chant, 2001; Federiuk and

Allen, 1996]. Here, the coordinates and symbols of horizontal (crossshore) wavenumber

1 With respect to NI oscillations, subinertial current (defined as motions with frequencies lower than 1/30

cph in the next chapter, where the local inertial frequency is 1/19.6 cph in the study region) are persistent

and act as a background current.

3

Figure I-1. Schematic diagrams for evolution of near-inertial wave energy in the coastal

region under the intermittent wind work at surface, density stratification, and steep

bottom slope (a) without and (b) with subinertial motions that accompany nearshore

coastal front and associated current shear.

4

k , vertical wavenumber m , and alongshore subinertial current V are detailed in

Chapter II and Appendix I. Presence of subinertial current shear changes the

background vorticity from f to eff

f . The NI waves which are generated or forced at a

frequency ω , are free to propagate both horizontally and vertically in the region where

efff>ω (The two terms in the right hand side of Eqn. I-1―22

2

m

k

f

N and

m

k

z

V

∂

∂ are small

compared to eff

f in this coastal problem). However, the propagation can be blocked in a

region where efff

5

effective Coriolis frequency (so horizontal shear of subinertial current) [Chant, 2001;

Federiuk and Allen, 1996], direction of NI wave propagation is affected by the

subinertial motions. Indeed, Davies and Xing [2005] and Davies and Xing [2002]

illustrate appreciable spatial variability in NI wave energy relevant to the NI wave

behavior, particularly in a case of coastal front (subinertial shear). In such numerical

studies, the NI waves are trapped and the energy leaks to depth on a negative vorticity

side whereas those generated on a positive vorticity side of the front propagate rapidly

away from the coastal region. The roles of subinertial current shear on the NI wave

behavior are essentially consistent to those of mesoscale circulations in the open ocean.

Besides the nonlinear interaction between the NI waves and subinertial motions, there

are other processes affecting distinct NI oscillations in the coastal region, contrasts to

those in the open ocean. In a stratified coastal ocean, coastal boundary (as a vertical

wall) makes a significant role on the pattern of NI oscillations. Presence of coastline

produces Ekman suction leading to internal pressure gradient, and NI waves are

generated even when the wind is spatially uniform [Davies and Xing, 2005]. No-normal

flow condition at the coastline gives convergence or divergence at the upper ocean

currents in the crossshore direction, which rapidly propagates offshore as a barotropic

signals, and subsurface NI oscillations phase shifted by 180 degrees from those at the

upper ocean [Millot and Crepon, 1981; Pettigrew, 1981; Kundu et al., 1983; Tintore et

al., 1995; Chen et al., 1996; Shearman, 2005].

However, the situations are much more complex when the coastal boundary is

considered as a sloping bottom, not a vertical wall. The NI waves generated near the

coastal boundary due to the Ekman suction can be reflected on the sloping bottom

which redistributes the NI wave energy in the coastal region, particularly, on a steeply

6

sloped region [Eriksen, 1998; Eriksen, 1982]. Bottom reflection of NI waves has been

identified as a plausible mechanism to cause downward phase propagation of NI waves

(which means upward energy propagation that implies the source of energy at the

bottom) in moored current measurements of opportunity off the east coast of Korea

[Kim et al., 2005b; Lie, 1988].

In particular, the role of sloping bottom on NI wave behavior becomes even more

complex in the case including the nonlinear interaction with subinertial motions, when

compared to the case without subinertial motions. Numerical model results with sloping

coastal boundary instead of vertical wall indicate significant influence of stratification

structure (background current shear) within a weak coastal front [Davies and Xing,

2005]. Moreover, Xing and Davies [2003] also shows controlling effects of sloping

coastal boundary on the generation and propagation of NI waves when the subinertial

motions are included. However, such combined effect of sloping bottom and subinertial

motion are still poorly understood and mostly confined to the theoretical level and not

widely investigated with observations (Figure I-2).

b. Coastal region off the east coast of Korea

In spite of many numerical and theoretical studies on the effects of sloping coastal

boundary (bottom slope) and subinertial current shear (nearshore coastal front) on NI

wave behavior, as shown in previous subsection, there are only few observational

studies relevant to the processes (Figure I-2) mainly due to the lack of high-resolution

(both in space and time) current measurements in the coastal region. Chen et al. [1996]

and Shearman [2005] described cross-shelf distribution of NI kinetic energy (hereafter

KE) from current moorings on the Texas-Louisiana shelf and New England shelf,

7

Figure I-2. Previous theoretical/numerical model studies and observational studies

about the effects of coastal boundary, and the combined effects of sloping bottom and

background (subinertial) current shear (or nearshore coastal front) on the near-inertial

wave behavior in the coastal region.

8

respectively. The characteristics of NI oscillations on the two shelf regions are much

similar, in a sense that they are surface-intensified with maximum values near the shelf

break decaying gradually toward the coast but rapidly offshore, as predicted by two-

dimensional, linear, flat-bottom, two-layer, coastal wall model [Shearman, 2005]. On

the other hand, highly heterogeneous distribution of subsurface NI KE is observed as

surface homogeneous energy provided by local wind work radiates toward the

thermocline on the New Jersey inner shelf during an upwelling period [Chant, 2001]. In

relation to the concentration of NI energy offshore the upwelling jet on the New Jersey

inner shelf, Chant [2001] discussed nonlinear interaction of NI waves with subinertial

shears. In addition, Shearman [2005] also discusses the roles of subinertial vorticity on

NI waves emanating from the coastal boundary and shifted NI oscillations observed on

the New England shelf.

However, it is important to note that those observational results are all derived from

the observations on the broad shelf regions where the bottom slope is relatively gentle.

In a narrow shelf region with steep sloped bottom, horizontal direction of NI waves near

the coastal boundary may become more important for the NI KE distribution because

types of bottom reflection are determined as a bottom slope in the horizontal wave

direction compared to the wave slope, i.e. backward bottom reflection would occur

when the bottom slope is steeper than the wave slope. Importance of using a three-

dimensional model with bottom topography has undoubtedly been emphasized in the

coastal region [Xing et al., 2004]. The NI oscillations on the steep sloped coastal region

must be not simple due to strong interactions of NI waves with sloping bottom as well

as those with subinertial current shear, as well implicated by recent model results

[Davies and Xing, 2005].

9

Nearshore coastal region off the east coat of Korea is ideal to examine the effect of a

steeply sloping coastal boundary on NI wave behavior as the slope is as large as

approximately ten times (0.02, Figure I-3) of the slopes in other coastal region studied

before, i.e. inner New Jersey shelf, New England shelf, and Texas-Louisiana shelf. Kim

et al. [2005b] analyzed current data from a mooring in this coastal region for few

months in 1999 and found that the observed NI oscillations are partly generated by local

wind but some of the observed NI oscillations, in particular, those of downward phase

propagations (upward energy propagations) can not be accounted for with the linear,

point model forced by local winds. They attributed the reason of model failure in

simulating the observations into remote energy source that propagates upward through

the forward bottom reflection in the horizontal direction nearly parallel to the coastline

(alongshore direction) as also suggested by Lie [1998] from another mooring current

measurements in the slope region off the east coast of Korea. However, the combined

effects of subinertial current shear and sloping coastal boundary on NI wave behavior

are not yet investigated with the observations of high spatial and temporal resolutions.

Detailed descriptions on the NI oscillations in the steeply sloped coastal region under

time varying subinertial shear, i.e. coastal upwelling/downwelling jets, thus, need to be

better understood in relation to the interactions between the NI waves and subinertial

current shear and between the NI waves and sloping bottom. It is a motivation of this

study.

2. Purpose

10

Figure I-3. Location and bottom topography in the study area. Here, the coastal area of

intensive observations which corresponds to the domain of Figure II-1 are marked as a

small box in left map and a dashed box in right map. The large box in left map

coincides to the domain of right map. The contours in right map are depths in meter.

11

Overall purpose of this study is on the better understanding of NI oscillations in the

coastal region, particularly with steep sloped coastal boundary and time-varying

(subinertial) conditions of background current shear. Basically, wind-induced mixed

layer inertial motion needs to be addressed prior to investigate the NI wave behavior

associated with background current shear and sloping bottom. With a simple linear

(damped slab) model, the NI oscillations observed in the region are simulated and the

discrepancy of model results is further reasoned and discussed. Then, the behavior of NI

waves is examined under typical background conditions considering bottom reflection

near the steeply sloping coastal boundary. Physical processes suggested by previous

numerical and theoretical works are re-examined with the observations in the coastal

region. Suggestions by previous observations are also improved by comparing them

with the observations of this study under more sophisticated physical configurations, i.e.

several different conditions for the background current and bottom slope. The hope is

that dynamic interpretations on mechanics accounting for the observations in this region

help to provide new physical insights on the processes controlling the coastal NI

oscillations.

The focus of this thesis is on the mechanics how the NI oscillations increase at a

certain depth of a certain location in the coastal region for a certain period. Whole

process is still unrevealed and only partly understood at theoretical level. They are even

not widely verified with in-situ observations mainly due to the lack of long-term (at

least a few years) and high resolution (in time and space) current measurements.

Therefore, this study is concerned with the NI oscillations observed from 1999 to 2004

in the region with temporal, horizontal, and vertical resolutions of few minutes, few

kilometers, and few meters, aiming at clarifying the followings.

12

1) Spatio-temporal structure of the NI oscillations observed in the coastal region off

the east coast of Korea

2) Wind-induced mixed layer inertial motion, and interactions between the NI waves

and subinertial current shear and between the NI waves and sloping bottom

3) Major causes for local change of subsurface NI KE in the region

3. Outline

This thesis consists of eight chapters. The background and motivation are contained

in Chapter I. In particular, the previous studies on the processes involving the NI waves

in a stratified coastal region with subinertial shear and sloping bottom are briefly

reviewed. Three objectives of this study are stated with the overall purpose and the

thesis outline in this chapter.

In Chapter II, instruments, field experiments, and preliminary data processing are

detailed. Time series data acquired using an ocean monitoring buoy system, and other

data obtained through several field programs are introduced. The coordinates and data

processing conducted prior to the analysis are preceded in this chapter.

The NI oscillations observed in the coastal region from 1999 to 2004 are described in

Chapter III, which are further examined in the Chapter IV, V, and VI. In Chapter III, the

observed NI oscillations are characterized and classified with vertical structure of NI

currents, horizontal ellipse shape of NI oscillations at depths, vertical profiles of NI KE,

etc. Wind-induced, local generations of mixed layer NI oscillations are detailed and

addressed using a simple linear (damped slab) model in Chapter IV. Possible causes for

13

discrepancy of the model are also speculated in this chapter. In Chapter V, propagation

and reflection of NI waves are investigated in the context of inertio-gravity wave theory

by further analyzing current data obtained under three different conditions: upwelling,

downwelling, and transition cases. Three-dimensional ray paths of NI wave energy

radiations for the cases are also provided in this chapter. Finally, the energetics and the

major source of local change of subsurface NI KE in the region are deduced in Chapter

VI with estimation of horizontal energy flux from the observations.

Results of the four chapters (Chapter III, IV, V, and VI) are discussed in Chapter VII

comparing them with those in four other coastal (shelf) regions. Possibility of wave-

wave interaction of NI waves with semi-diurnal internal tides and significance of NI

oscillations on intermittently enhanced localized mixing are further discussed in this

chapter. At last, summaries and conclusion are presented in Chapter VIII followed by

underlying questions and suggestions for future study.

14

Chapter II. Field Measurements and Data

1. Real-time ocean monitoring buoy

An ocean monitoring buoy is developed and successfully applied in the region, which

was originally located about 8 km off the east coast of Korea since 1999 in the depth of

100 m (N2, Figure II-1), and the location was changed to S2 (water depth of 130 m)

since 2002 (Figure II-1). This buoy system is equipped with meteorological sensors,

several (SBE37) Conductivity-Temperature-Depth (CTD) sensors, and (RD Instrument)

300 kHz workhorse acoustic Doppler current profiler (ADCP) to collect continuous

time series data of wind speed and direction, air pressure and temperature, and physical

properties (temperature, salinity, and pressure) and currents at depth levels. The buoy

system (ESROB; East Sea Real-Time Ocean Buoy) and technologies applied to the

buoy is described in Nam et al. [2005a] with recent improvement.

With the high temporal sampling interval of 10 minutes, the currents were measured

at four depth levels from 26-50 m (every 8 m) in 1999, twenty depth levels from 5-100

m (every 5 m) in 2000-2002, and twenty-six depth levels from 5-130 m (every 5 m) in

2003-2004. Water temperature and salinity were measured every 10 minutes at four

depth levels (20, 40, 60, and 80 m) in 2000, five depth levels (5, 20, 40, 60, and 100 m)

in 2001-2003 and 2004, and eight depth levels (5, 10, 20, 40, 60, 80, 100, and 125 m) in

2003. Wind speed and direction were also measured every 10 minutes at the top of the

buoy (2.1 m above sea level). Due to the maintenance problems of the buoy system,

data were not collected for some winter months. Measurements of the ESROB are

summarized in Table II-1.

15

Figure II-1. Positions of Eulerian measurements (N2, S1, S2, and S3), CTD stations (1-

14) with bottom topography (in meter) in the coastal area of extensive observations

marked in Figure I-3. The water depths at S1, N2, S2, and S3 are 20, 100, 130, and 190

m, respectively. The ESROB, PKNUB, TRBM and ESOREC denote the East Sea Real-

time Ocean Buoy, Pu-Kyung National University Buoy, and the East Sea Ocean

REsearch Center (37oN 35’). The photo of instruments and sectional view of the

measurements are shown in right panel.

16

Table II-1. Periods, position, sampling interval, depth ranges or levels of ESROB (East

Sea Real-time Ocean Buoy) measurements.

Depth of current

Measurements

(m) Year Period Position

Sampling

Time

interval

(min.) range interval

Depth of

temperature/

salinity

measurements

(m)

April 25-June 27 N2 10 26-50 8 None 1999

August 26-September 22 N2 10 5-100 5 None

April 7-May 30 N2 10 5-100 5 20, 40, 60, 80 2000

June 14-August 13 N2 10 5-100 5 20, 40, 60, 80

2001 April 1-September 25 N2 10 5-100 5 5, 20, 40, 60, 80

April 25-June 19 S2 10 5-100 5 5, 20, 40, 60, 100 2002

June 28-August 19 S2 10 5-100 5 5, 20, 40, 60, 100

2003 January 12-October 22 S2 10 (1)2 5-130 5 5, 10, 20, 40, 60,

80, 100, 120

2004 April 17-September 2 S2 10 (1) 5-130 5 5, 20, 40, 60, 100

2 Currents, temperature, and salinity were measured every minute for specific periods of few days since

2003.

17

Similar buoy system (PKNUB; PuKyung National University Buoy) was operated

temporally at S3 (water depth is 190 m) from April 26 to May 20, 2002 (Figure II-1).

This buoy is also equipped with meteorological sensors, a (RD Instrument) 300kHz

workhorse ADCP and five (SBE37) CTDs to measure wind speed and direction,

currents from 5 to 100 m at twenty depth levels (every 5 m), and water temperature and

salinity at five depth levels (5, 20, 40, 60 and 100 m), respectively.

2. Field experiments

The point for Eulerian current measurements was added at S1 (Figure II-1) using (RD

Instrument) 1200 kHz workhorse ADCPs equipped at the Trawl Resistant Bottom

Mount (TRBM) through field experiments in May-June 2002. Water depth at S1 is 20 m,

and the depth range of current measurements is 9-18.75 m (every 0.25 m). In this thesis,

Eulerian current measurements simultaneously collected at three different sites (S1, S2,

and S3) in May 2002 are used to examine spatio-temporal structure of NI oscillations

although the current measurements at N2 and S2 from 1999 to 2004 are primarily

analyzed. The resolutions of Eulerian current data in May 2002 are 10 minutes

temporally, few meters vertically, and few kilometers horizontally.

Besides the current data, the time series measurements of wind, temperature and

salinity at N2, S2, and S3 are used in the analysis. The observed wind data are

supplemented with the European Center for Medium-range Weather Forecast

(ECMWF) reanalysis wind stress product (ERA40) around the study area of which the

time interval is 6 hours and grid size is 0.5 degree. Time series of density is obtained

from the temperature and salinity measured at each depth of N2, S2 and S3.

18

In addition, from spring to summer of 1999 and 2000, profiles of temperature and

salinity are acquired by casting CTD at 14 stations along the three lines (N-line, S-line,

and alongshore line between the two lines) (Figure II-1) thirty one times in total

(seventeen times in 1999 and fourteen times in 2000). The horizontal distance between

neighboring stations is 1 mile and the irregular time intervals of the CTD measurements

are from 5 to 21 days. The CTD data are used to evaluate section structures of

temperature and salinity (so density), and geostrophic current with horizontal shear of

background current.

3. Data processing

Horizontal current vector at each depth level and wind vector (W ) are separated into

the alongshore (y) and crossshore (x) components where the alongshore direction is 30

degrees anticlockwise from the north (Figure II-1). Wind stress is calculated from the

alongshore and crossshore wind data using a simple quadratic form, i.e. WWC airDρτ =

where the constant drag coefficient 3104.1 −×=DC and air density airρ . Gaps in current

data possibly due to the vertical migration of zooplankton are filled with vertical

interpolation to obtain hourly time series data at all the depth levels (Appendix II). Here,

cubic-spline method is applied for the vertical interpolation to produce data for the

periods of blank data (mostly night time below 60 m). Without this vertical interpolation

prior to apply successive analyses, these scanty data in time cause over-smoothing of NI

oscillations in the lower levels when they are band-pass filtered (Figure II-2). All time

units are days from January 1, 1999 that is set to Day 1.

Most spectra of alongshore and crossshore currents show clear peaks at diurnal, NI,

19

Figure II-2. Crossshore currents measured at 55, 65, 70, and 75 m of S3 before (black)

and after (blue) vertical interpolation. The data gap at 65, 70, and 75 m in night can

cause over-smoothing of near-inertial currents when they are band-pass filtered.

20

and semi-diurnal periods which are 24, 17-20 (the local inertial period is about 19.6

hours), and 12 hours, respectively, and smeared peaks at subinertial periods (defined

here as periods longer than 30 hours). In particular, at the NI period, the spectral

densities are much different among the dataset depending on depth and time of the

measurements, which is contrast to the case of diurnal and semi-diurnal peaks (Figure

II-3). For example, the spectral densities of crossshore currents measured at 50 m of S2

in 2003 are much higher (> 500 cm2/s

2 hour) at the NI frequencies than those at the

same location in 2001 (< 200 cm2/s

2 hour) or those at 80 m of S2 (

21

Figure II-3. Auto-spectra of crossshore currents measured at 50 m of S2 in 2003 (thick

black), 80 m of S2 in 2003 (thin black), and 80 m of N2 in 2001 (gray) and filter

response function for low-pass (gray) and band-pass (black) filters used in the study.

The criteria of subinertial and near-inertial frequencies that are 30 hours and near 19

hours (17-20 hours) respectively are noted as vertical gray lines.

22

Chapter III. Characteristics of Near-inertial

Variability off the East Coast of Korea

1. Vertical and temporal variations

The NI currents (band-pass filtered currents) observed at N2 and S2 in the region are

intermittently amplified for a few days or a week at depth raging a few tens of meters

(Figure III-1), indicative of highly episodic and heterogeneous NI oscillations as

expected from the comparison of spectra in the previous chapter. Temporal scale (2-11

days) of the NI oscillations implies the relevance to the subinertial current shear as well

as subinertial variability of local wind stress. Individual amplifications when the NI

current exceeds 3 cm/s is taken as an event and totally forty events are selected during

the whole observation period from 1999 to 2004. For example, the NI oscillations are

temporally enhanced in May 2002 (Days 1215-1222 and Days 1224-1228), July 2002

(Days 1285-1292 and Days 1296-1301), and May 2003 (Days 1590-1595) (Figure III-1).

The periods correspond to event (13) and (14), (16) and (17), and (21).

The NI oscillations during the events are characterized with vertical direction of

phase propagation in time, horizontal orientation of principal oscillations, vertical

distribution of the amplitude (or kinetic energy), etc. Phase of NI oscillations propagate

mostly upward with time as case of the events (14), (16) and (17) whereas downward as

the events (13) and (21) (Figure III-1). NI oscillations are enhanced mostly in the

crossshore direction for the case of events (16) and (17) whereas the alongshore

direction for the event (21). Most NI oscillations are confined near the surface as during

Figure III-1. Time-depth contours of near-inertial currents in the alongshore (v) and crossshore (u) directions where the time units are days

from January 1, 1999. Total 40 events are indicated as bracketed numbers when and where the NI currents are significantly (> 3 cm/s)

enhanced.

23

24

the events (14) and (21) but significant NI oscillations are also found in the interior as

the case of event (13), (16), and (17). It is necessary that the NI oscillations during the

forty events are quantitatively characterized and classified into several types having

common characteristics, which is presented in the remaining part of this chapter.

2. Complex empirical orthogonal function (CEOF) analysis

Vertical and temporal structure of NI current observed at N2 and S2 are examined

through a complex empirical orthogonal function (CEOF) analysis. The analysis

separates the data into the depth-dependent, empirical orthogonal modes. Each mode n

has a vertical eigenfunction of horizontal current vector nA (or CEOF), corresponding

time coefficient nB , and an associated variance (expressed in percentage of total

variance). Thus the CEOF representation of NI current u is

∑=

=N

n

nn tBzAtz1

)()(),(u .

First four CEOF modes ( 1A - 4A ) accounting for 80% of total NI variance show the

magnitudes decreasing in depth (Figure III-2). One interesting finding is that the current

vectors of 1st and 2nd CEOFs (56%) rotate clockwise with depth, whereas those of 3rd

and 4th CEOFs (24%) rotate counterclockwise (Figure III-2). This indicates upward

phase propagation (currents at the lower levels lead) of 1st and 2nd CEOFs and

downward phase propagation (currents at the upper levels lead) of 3rd and 4th CEOFs,

since they rotate clockwise in time at all the depth levels. As the vertical components of

phase velocity and group velocity are opposite for the inertio-gravity waves [Kundu,

25

Figure III-2. Vertical profiles of first four modes (A1, A2, A3, and A4) complex

empirical orthogonal functions (CEOFs) accounting for 80% of total variance indicate

that the magnitudes of near-inertial currents generally decrease with depth. The current

vectors of 1st and 2nd modes CEOFs (56%) rotate clockwise whereas those of 3rd and

4th modes CEOFs (24%) counterclockwise with depth, indicative of downward and

upward propagations of near-inertial energy, respectively.

26

1990], the upward and downward phase propagations reflect downward and upward

energy propagations, respectively.

Time coefficients ( 1B - 4B ) of the four CEOF modes clearly show intermittent

modulations of NI oscillations during the events (Figure III-3). However, there are some

events when no significant modulation occurs in the time coefficients of 1st and 2nd

modes but those of 3rd and 4th modes. This is in the case of events (6), (8), (13), (21),

(24), (27), (29), (36), and (39) when the downward phase propagation (upward energy

propagation) is prevailed in the region (Figure III-3 right). On the other hand, upward

phase propagation (downward energy propagation) is dominant in the events (2), (3),

(4), (5), (9), (11), (12), (14), (15), (16), (17), (19), (20), (22), (23), (25), (26), (28), (30),

(31), (35), and (38) (Figure III-3 left). The downward phase propagation of NI

oscillations during the event (13), and (21) and the upward phase propagation during the

event (14), (16), and (17) was consistently pointed out in the previous section.

3. Horizontal ellipse

a. Polarization

Horizontal hodograph of NI current can be quantified by determining the polarization

(ϕ ) of NI current ellipse in a horizontal plane as an angle of major axis orientation from

the east in degrees, that is

−

= −22

12tan

2

1),(

vu

uvtzϕ .

In Figure III-4, red and blue colors denote that the NI oscillations are polarized close to

the crossshore (~ 30 degrees) and alongshore (~ 120 degrees) directions, respectively.

Figure III-3. Time coefficients of first four modes (B1, B2, B3, and B4) complex empirical orthogonal functions (CEOFs) where those of

1st and 2nd modes CEOFs and 3rd and 4th modes CEOFs are shown in the left and right panels, respectively. Intermittent modulations

of the time coefficients during the events are separated as periods of B1 and B2 dominant or those of B3 and B4 dominant.

27

28

For example, the NI oscillations observed during the events (16) and (17) are polarized

mostly in the crossshore direction whereas those during the event (21) in the alongshore

direction (Figure III-4). This is also consistent to the descriptions in section 1 of this

chapter. The polarization of NI current ellipse is important to evaluate the horizontal

directions of NI waves, which are provided in Chapter V.

b. Ellipticity

Shape of NI current ellipse is also quantified with the ellipticity ( ε ), or ratio of minor

axis to major axis of the ellipse. If the ellipticity is close to unity (zero), the ellipse has

circular (rectilinear) shape. For example, the shape of NI current ellipse is more

rectilinear during the events (16), (17), and (21) whereas more circular for the case of

events (13) and (14) (Figure III-5). Rectilinear shape of NI current ellipse implies that

the NI oscillations greatly depart from the pure inertial motion that has perfectly circular

shape of NI current ellipse. The ellipticity of NI current ellipse is another important

characteristics of NI oscillations for examining the mechanics causing them, which are

detailed in next three chapters (Chapter IV, V, and VI) with further analysis.

4. Kinetic energy

a. Vertical and temporal variations

The NI KE per unit mass (cm2/s

2) is calculated from the NI current at each time and

depth of N2 and S2 as

( )222

1vuKE +=

29

Figure III-4. Time-depth contours of the polarization of near-inertial current ellipse in

the horizontal plane that is defined as an angle of major axis orientation from the east in

degrees. The events are separated as those when the polarization is close to crossshore

direction (red) and alongshore direction (blue). Here, the polarization is shown when

and where the near-inertial currents exceed 3 cm/s.

30

Figure III-5. Same as Figure III-4 but the ellipticity of near-inertial current ellipse that

is defined as a ratio of minor axis to major axis from zero to unity. Similarly, the events

are separated as those when the ellipticity is close to zero (rectilinear, red) and unity

(circular, blue).

31

as shown in Figure III-6. Most high KEs are confined to the upper levels near the

surface and the KE level is usually low in the interior. However, the interior KE

becomes significant during the event (3), (11), (13), (16), (17), (20), (33), (34), (36),

(39), and (40). For example, the NI KEs during the event (16) and (17) exceed 10 cm2/s

2

below 20 m depth. In such cases, the NI KEs are higher at the interior than the upper

levels although such inequality are opposite during the cases except those events.

b. KE EOF

In order to quantify the vertical distribution of NI KE in the region, from the time

series of vertical NI KE profiles in 2000-2004, vertical and temporal structures of NI

KE are examined with EOF analysis. This analysis is the same as CEOF except the EOF

is a scalar function, i.e. KE. The EOF representation of NI KE (hereafter KE EOF) is,

thus,

∑=

=N

n

nn tFzEtz1

)()(),(KE .

Here, notice that the KE EOF modes are not correspond one-to-one to the squared

CEOF modes of NI current because the modes are separated as the NI KE

eigenfunctions, i.e., 1E , 2E , 3E ,… NE be orthogonal, not the NI current eigenfunctions.

First four modes KE EOFs ( 1E - 4E ) explain 80% of total variance in NI KE observed

at N2 or S2 in the region from 2000 to 2004. However, the vertical structure of 1st

mode KE EOF ( 1E ) accounts for only 45% where the large variances are confined to the

upper levels and they decrease rapidly in depth (Figure III-7). Note that all the four

CEOFs ( 1A - 4A ) of NI current (accounting for 80% of total variance in NI current) have

structures where the magnitude decreases rapidly in depth (Figure III-2), corresponding

32

Figure III-6. Time-depth contours of near-inertial kinetic energy per unit mass (cm2/s

2),

where the 40 events are marked as bracketed numbers. Though the kinetic energy is

enhanced at the upper levels during many events, there are the events when the kinetic

energy is significant in the interior as denoted with boxed numbers.

33

Figure III-7. Vertical structures of first four modes EOFs (E1, E2, E3, and E4) of near-

inertial kinetic energy, which account for 80% of total variance. First mode EOF of

which the most variances are confined at the upper levels explains only 45% and the

three other modes EOFs (35%) have the structure of significant interior variations of

kinetic energy.

34

to only the 1st mode KE EOF ( 1E ). The 2-4th modes KE EOF ( 2E - 4E ) accounting for

the 35% of total variance in NI KE represent significant NI KE variations in the interior

of the water column at N2 or S2 (Figure III-7). In particular, during the event (3), (11),

(13), (16), (17), (20), (33), (34), (36), (39), and (40), the time coefficients ( 2F - 4F ) of 2-

4th modes KE EOFs become relatively important compared to those ( 1F ) of 1st mode

KE EOF (Figure III-8). This is also consistent to the qualitative descriptions in section

4a of this chapter.

c. Depth-integrated near-inertial kinetic energy

The NI KE is integrated over the depth from the surface to 100 m and the mean

density 0ρ (calculated by averaging density over depth at N2 and S2) is multiplied to

estimate depth-integrated KE (hereafter DKE) per unit area of water column in J/m2 as

below.

[ ]∫− +=0

22

0 ),(),(2

1)(DKE

Hdztzvtzugt ρ

Here, the bottom depth H is fixed to 100 m except for the case of year 1999 where the

KE is integrated from 26 to 50 m. The time series of DKE is shown in Figure III-9.

Most striking feature of temporal DKE variations from 1999 to 2004 is that there is

no clear seasonal pattern (Figure III-9). For example, the DKE in the region is largely

enhanced in spring of 1999, 2000, 2002, and 2004, whereas it is not in spring of 2001

and 2003 (Figure III-9). Similarly, the large (> 80 J/m2) DKE is observed in July of

2002 and 2003 (correspond to the event of (16), (17), (23), and (24)) while the DKE in

July of 2000, 2001, and 2004 is relatively weak (Figure III-9). Particularly strong (> 80

J/m2) DKE is observed in May 1999, April-May and September 2000, May and July

35

Figure III-8. Time coefficients of first four modes (F1, F2, F3, and F4) EOFs of near-

inertial kinetic energy where the peaks during the events (numbered) are separated as

those when the 1 mode EOF is dominant and those when the 2-4 modes are comparable

(boxed numbers).

36

Figure III-9. Time series of depth-integrated near-inertial kinetic energy per unit are in

J/m2, where 40 events are marked as bracketed numbers. Particularly large (80 J/m

2)

depth-integrated kinetic energy is observed in the region during the events denoted as

shaded numbers. Temporal structure of such events do not show clear seasonal pattern.

37

2002, July to November 2003, and May 2004 (Figure III-9). In contrast, in June 1999,

July 2000, April to June 2001, May to June 2002, February to June 2003, and June and

August 2004, relatively weak (< 40 J/m2) DKE is mostly observed (Figure III-9). This

non-seasonal pattern of DKE implies that the mechanics causing the NI oscillations in

the region are not simple, i.e. wind-induced mixed layer inertial motion which generally

has clear seasonal variations (more enhanced in summer than in winter) due to seasonal

pattern of mixed layer variability.

5. Crossshore structure (May 2002)

a. Spatial and temporal variations

By analyzing NI current simultaneously observed at S1, S2, and S3 in May 2002,

crossshore structure of NI oscillations and NI KE is examined. The NI currents

observed at 10-20 m of S1, 5-100 m of S2 and S3 and the NI KE during the period of

May 2002 from Day 1216 to Day 1228 (correspond to the event of (13) and (14)) are

compared in depth-time domain (Figure III-10). As shown in section 2 of this chapter,

the downward and upward phase propagations are dominant at S2 for the event (13) and

(14), respectively. And as revealed in section 4 of this chapter, the NI oscillations at S2

are surface intensified during the event (14) whereas they are significant in the interior

in the event (13). The shapes of NI current ellipses at S2 are relatively circular during

the two events (Figure III-5) and the polarizations are close to alongshore and

crossshore directions for the (13) and (14), respectively (Figure III-4). However, in spite

of close separations (few km) among the locations of S1, S2, and S3, the NI oscillations

38

Figure III-10. Time-depth contours of crossshore (upper left) and alongshore (upper

right) near-inertial currents and the kinetic energy (down right) observed at S1, S2, and

S3 for Days 1216-1228 (from April 30 to May 12, 2002) where the vertical lines

separate the periods of 2-4 days named Leg-I, II, III (corresponding to the event (13)),

and IV (events (14)).

39

at S1 and S3 have quite different characteristics from those at S2, in vertical phase

propagation in time, vertical distribution of the NI KE, etc (Figure III-10). For example,

NI KE is very weak at S1 during the whole period and high NI KEs are confined to the

upper levels of S3 during the event (13) whereas those are spread in the interior of S2

(Figure III-10).

The period is separated into four Leg periods (Leg-I, II, III, and IV) of 2-4 days

according to the characteristics of NI currents at depths of S2 and S3. During Leg-I

(Days 1216-1219), strong surface intensified NI oscillations are observed at S3 only,

which show upward phase propagation although mild NI oscillations occur at lower

levels of S2 and S3 during Leg-I (Figure III-10). The NI oscillations during Leg-II show

dominant downward phase propagation from 15 to 100 m of S2 and from 10 to 35 m of

S3 (Figure III-10). During Leg-II, vertical direction of phase propagation is upward

below 40 m of S3 (Figure III-10). Then, only weak NI KE remained near the surface of

S2 and S3 during Leg-III, where the NI current still show downward phase propagation

(Figure III-10). In Leg-IV (correspond to event (14)), the NI oscillations again

significantly enhanced near the surface of S2 and S3, where the vertical direction of

phase propagation changes to upward (Figure III-10). The thickness of strong NI

oscillations during Leg-IV is doubled at S2 compared to that at S3 (Figure III-10).

Vertical direction of phase propagation at three depths of 30, 50, and 70 m of S2 and S3

are summarized in Table III-1 for the Leg-I, II, III, and IV.

b. Sectional KE EOF

40

Table III-1. Vertical directions of phase propagations of near-inertial currents during

Leg-I, II, III, and IV where the directions only for the cases of enhanced (3 cm2/s

2) near-

inertial kinetic energy are shown.

Vertical direction of phase propagation

Depth Station Leg I Leg II Leg III Leg IV

30 m S2 - down down up

50 m S2 up down - -

70 m S2 down down - -

30 m S3 up down down up

50 m S3 up up - -

70 m S3 - - - -

41

The NI KEs observed at S1, S2, and S3 in May 2002 are separated into modes of

sectional KE EOF ( ),( zxGn ) and corresponding time coefficient ( )(tH n ). The sectional

KE EOF representation of NI KE across the coastal region is,

∑=

=N

n

nn tHzxGtz1

)(),(),(KE .

The sectional KE EOF analysis indicates that first three modes of sectional KE EOF

explain 81% of total variance of the NI KE observed during the Leg-I, II, III, and IV.

The first three sectional KE EOF structures reveal that the KE variations are negligible

at S1 and that they are consistent between S2 and slightly (few or few tens of meters)

shallower depth of S3 (Figure III-11 down). Positive 1st mode of sectional KE EOF is

dominant during Leg-I whereas both negative 1st mode and positive 2nd mode become

important during Leg-IV (Figure III-11 up right). Cross-sectional structure of NI KE

variations are shown as schematics in Figure III-11 (up left).

42

Figure III-11. Schematic sectional view of crossshore structure of near-inertial energy

(up left), first three sectional EOFs (G1, G2, and G3,) of near-inertial kinetic energy

(accounting for 81% of total variance during the Leg-I, II, III, and IV) (down), and the

associate time coefficients (H1, H2, and H3,) (up right) where the Leg-I, II, III, and IV

are divided.

43

Chapter IV. Wind-induced, Local Generations of

Mixed Layer Near-inertial Oscillations

1. Local wind variability

a. Buoy wind stress

Time series of alongshore and crossshore wind stress ( yτ , xτ ) estimated from buoy

wind measurements, are shown in Figure IV-1. It is known that northwesterly winds

associated with the Asian winter monsoon are persistently dominant so that the

southeastward (negative alongshore) wind stress is dominant from November to

February in the region every year. However, from March to October, the direction of

wind is quite variable due to the frequent (in a few or few tens of days) passages of

mesoscale weather system without such strong persistent winds [Nam et al., 2005b].

This frequent change of wind direction cause high variability of wind stress both in the

alongshore and crossshore directions in the coastal region (Figure IV-1). The

magnitudes of alongshore and crossshore wind stresses are mostly less than 0.2 N/m2

but they sometimes exceed it particularly during the local passage of storms such as

Days 609-610 (typhoon Prapiroon on August 31-September 1, 2000), Days 1715-1718

(typhoon Maemi on September 11-14, 2003), Days 2011-2013 (typhoon Mindulle on

July 3-5, 2004), Days 2405-2407 (typhoon Namtheun on August 1-3, 2004), etc. A

thorough description of wind stress in the region is provided by Nam et al. [2005b]

44

Figure IV-1. Time series of alongshore (black) and crossshore (gray) wind stresses

from 1999 to 2004, measured at N2 (1999-2001) and S2 (2002-2004).

45

where seven kinds of wind dataset are analyzed to describe spatio-temporal variability

of wind stress.

b. Subinertial buoy wind stress and spatially-averaged ECMWF wind stress

The alongshore and crossshore wind stress estimated from buoy wind measurements

are low-pass filtered with half power centered at 30 hours to extract only subinertial

fluctuations. They are proven to have consistency with the ECMWF wind stress at the

nearest point for the subinertial periods [Nam et al., 2005b]. The ECMWF wind stress is

averaged over the area of 4 by 4 degrees shown in Figure IV-2, which contains 38 grid

points. From the two time series (low-passed buoy wind stress and spatially-averaged

ECMWF wind stress), the upwelling favorable and downwelling favorable wind

conditions are classified (Figure IV-2) which are noticed as cumulatively positive and

negative wind stresses, respectively, both in the alongshore and crossshore directions.

Time-integrated wind stress exceeds 0.2 Pa day in magnitude during those periods of

upwelling and downwelling wind conditions. Interesting point is that the upwelling and

downwelling periods show no clear seasonal pattern (Figure IV-2) as those of DKE in

the region (Figure III-9). Close relationship between the upwelling/downwelling

conditions and the DKE is detailed in Chapter V.

To quantify local non-uniformity of wind stress in the coastal region, time series of

low-pass filtered buoy wind stress and the spatially-averaged ECMWF wind stress are

compared in time domain. Significant (~0.2 N/m2) difference between the two wind

stresses occurs on May 1999, April and June to August 2000, April to May, late June,

and September 2001, July to August 2002, late January, April to May, July and

September 2003, etc (Figure IV-3). It is basic hypot

near-inertial current variability off the east coast of...

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