海洋科学技術センター試験研究報告　第35号　JAMSTECR, 35 (March 1997)

二重層海洋における内部波について（Ｈ）

緑川 弘毅＊1

流れが海底に砂漣をつくることは良く知られている。底質は沿岸においては海面の

波によって，沖合では流れによって移動するものと考えられている。

著者らの研究により，内部波によって起る海底付近の流れは，堅い海底の底質を洗

掘したり，直径数センチ以上もの石を動かすことが確かめられた。

沿岸での内部波は海岸線に向かって入射するが，内部波で起される流れは沖に向か

う。大きな振幅の内部波が陸棚で砕波するとき，それによる底質移動の効果は，水深

が時には数百メートル，あるいはそれ以上に及ぶことがある。

キーワード：内部波，内部潮汐，二重層海洋，水の運動，底質輸送，水温境界層，

塩分躍層

On Internal Waves in a Two-Layer Ocean Area (II)

Koki MIDORIKAWA*2

It is well known that the current generates sand ripples on the sea bottom. It is thought

that in shallow waters sand ripples are generated by the movement of water associtated

with surface waves, and in deeper waters by the current.

It was found that the horizontal motion caused by internel waves below the pycnocline

could transport stony sediments having the size of several centimeters or more in diameter,

and form big scale ripples on the hard bottom.

In coastal area, the internal wave direction is shoreward, and the flow caused by internal

waves is always offshore. The water motions generated by internal waves having large am-

plitude sometimes have a great effect of sediment transportation when the internal waves

break at shelf floor, though the shelf is at the depth of several hundreds meters or more.

Key Words : Intern] waves, Internal tidal waves, Two-layer ocean, Water movement,

Sediment transportation, Thermal boundary, Pycnocline

７

＊１　海洋観測研究部

＊２　Ocean Research Department

1 Introduction

Internal waves are the vertical oscillations of

pycnocline in sea water and the flows of water

which occur accompanied with internal waves. They

usually travel more slowly than surface waves, but

they may have a greater height and length. Internal

waves occur at surfaces between different density

layers within the sea, because the density difference

leads to a gravitational pressure restoring force if

fluid is displaced vertically. In a two-layer density

area, maximum amplitude of internal waves exists

at the boundary of the two layers, and decreases

linearly with distance above and below.

The nature of the thermocline is influenced by a

number of factors and therefore varies in depth and

magnitude from place to place and from time to

time. Strong stratifications are generally formed in

coastal areas, especially, near an estuary harbor.

The thermocline develops in late spring and becomes

stronger in summer.

The water motion over the crest of internal

waves is more active for the smaller thickness of

the upper layer and the effect of the motion reaches

the sea surface, consequently, the circulation of

water associated with the internal wave generates

convergences and divergences on the sea surface.

Divergences appears at the front of the crest and

convergences at the back of the crest of internal

progressive waves. The convergence has an effect on

the sea surface of reducing the surface tension, and

making capillary waves disappear, thus slicks are

formed at the active surface convergence zone. The

smoothing effect of slicks is mostly attributed to

the absorption of energy from the wind-produced

capillary waves by the alternate expansion and con-

traction of surface film.

The absence of wavelets in slicks gives it a glassy

appearance in contrast with surrounding ripples.

The slicks move shoreward parallel to the depth

contours at the same speed as the internal waves.

Assuming that there is no appreciable net transport

of sea water across a vertical section perpendicular

to the direction of wave propagation, the same volume

of water per unit width must pass over the crest as

８

under the trough, the horizontal velocities over the

crest and under the trough must be inversely pro-

portional to the respective thickness of both layers,

and the former increases with the increase of the

amplitude of the internal wave.

Horizontal velocities of flow generated by internal

wave motions were estimated theoretically and they

were partly confirmed by means of observations

(Midorikawa, K. (1975 °), Midorikawa, K. and N.

Sakakida (1996a")).

The authors have made observations of internal

waves at the innermost part of Suruga Bay by

means of measuring temperature fluctuations at

several subsurface layers. Of the bays and inlets

along the Japanese cost, Suruga Bay is the deepest.

It has an oval shape, opening to the Philippine Sea.

Along its major axis, the depth exceeds 1,000 meters,

gradually increasing to 3,000 meters at the mouth.

Near the head of the bay rises Mt. Fuji, 6,500 meters

high above the deepest part of the bottom of the

bay.

Suruga Bay contains many important harbours

and its sea suface is crowded with commercial vessels

and fishing boats. The Kuroshio flows south of the

bay from the west toward the east and the effects

of its fluctuations may be expected to intrude into

the bay in various forms. Internal waves are one of

them and it is an interesting and important problem

to infer the fluctuations of the Kuroshio from the

observation of internal waves generated by its adjust-

ment processes.

The internal waves are generated by various

causes. In order to be able to examine a special

mode of internal waves, therefore, knowledge of the

normal structure of internal waves in Suruga Bay is a

prerequisite. A systematic and continuous observation

of internal waves is not an easy task, especially in

a bay such as Suruga Bay where maritime traffic is

intense.

The duration of one series of measurements ranged

from several days to several weeks. Temperature

measurements at 4 or 5 levels were undertaken in-

termittently and the data amount in total up to

140 days. From the records of water temperature,

JAMSTECR, 35 (1997)

spectral energy densities of temperature oscillation

were computed for the range from the inertial period

to the V aisala period (Midorikawa and Miyazaki

(1977a3))， IvIidorikawa (1977b4)， 1977cS)， 1973bS

)， 1996c1)，

1996d紛)).

The computations were performed scparatcly for

longer-period waves (order of hours) and for short-

period Corder of minutes) waves. The general features

of the temperature spectra are similar to the velocity

spectra obtained by Ozmidof and Webster， i.e. ， except

for the marked peaks， the general trends of spectra

for both the higher and lower frequency ranges have

slopes nearly minus-five thirds power of the frequency

(f5/3).

Internal waves are subsurface waves found between

layers of different density or within layers where

vertical density gradients are present. They can

exist in any stratified f1uid， in the ocean and also

in the sky.

Regular waves in the sheet of altostratus clouds

are seen in Photo 1. Internal waves in the atmos-

phere have been detected by a variety of instru-

ments， microbarographs and wind recorders at

ground level， and long-term recordings of the scat-

tering of radar or sonar beams by sharνdensity

gradients in the high atmosphere.

ln the ocean， we can also see visible evidence of

internal waves (Photo 2). A thin layer of nearly

fresh water from a river spreads out in the estuary，

and the blowing wind may create internal waves at

the lower boundary of the thin fresh-water layer.

Sea surface slicks too are visible evidence of internal

waves. The absence of wavelets in a slick gives it a

glassy appearance in contrast to the adjacent rippled

water. A slick appears brighter than its surrounding

area because the smooth surface reflects the sky more

than a rougher one (Midorikawa (1995a勺， Photo 3).

2 Internal tidal waves

2.1 Internal tidal waves and internal tidal

currents

Tidal force is responsible for important tempera-

ture changes in the sea by causing advection of water

of a djfferent temperature， or by producing vertical

JAMSTECR， 35 (1997)

Photo 1 Regdar undulations in the sheet of alto-

stratus clouds.

Photo 2 B10wing wind may create internal waves at

the boundary of the thin fresh国 waterlayer.

Blue belts which occurred by upward

circulations from the under layer and yelluw

bands of the surface layer lined alternatly.

Photo 3 Sea surface slicks extended laterally on

bright stripes. We can see the scene sometimes

through thc window.

9

of kilometers which exhibit strong broclinicity，

vertical1y varying properties.

l.e，

without any appreciable tidal currents.

Measurements of the vertical structure of the

temperature， salinity and current have been made in

the inlet with the bottom depth of 100 meters of

Suruga Bay (Okamoto， M. and K. Midorikawa (1976

a8)) ， Midorikawa， K.(1995b1め)， Midorikawa， K. and

T. Miyazaki (1977♂)). In the figure， the variations

of these data of a periodic nature close to the

semidurnal oscillations suggest that the causes are

related to the tide CMidorikawa，K. (l973aω， 1977b4)

and 1977 c5)) ).

In the left side panel of Fig. 1 ， the magnitude of

the vertical variations of the main isotherm reaches

more than fifty meters. The vertical displacements

of water caused by internal waves are important

factors in water mixing and transport.

Internal waves， if they grow large as shown in

the figure， must break and dissipate their energy

into turbulent or eddy motions. 80 the distinction

between internal waves and turbulence may be an

arbitary one. The troughs of isotherms reached the

sea floor Caround 8 0' clock on 24th and 25th)， and

the speed of the flow caused by their wave motions

were thought to be decreased by the turbulence.

We can guess that the speeds sometimes exceed

one knot to the west (off shore direction) in the

bottom layer and also in the surface layer. The

water passing over the trough or under the crest is

funneled through the constriction and the water

motions will be strong.

In the current profile， maximum speed appears

simultaneausly under the trough and also over

trough in both layers Fig. 1， 2. In shal10w water，

horizontal water motions caused by larger height of

internal waves in each layer sometimes f10w in the

opposite direction， respectively， for the water mass

conservation of the inlet.

This means that the water mass-flow caused by

internal waves is large for the small inlet， and it

contributes much to the water circulation of the

inlet.

oscillations. When subsurface temperatures are plot-

ted with reference to time， considerable fluctuations

are always apparent with cycles corresponding to

tidal periods.

It is evident that extremely complicated currents

may be found if several internal waves of different

orders， different phases， and different tidal periods

are present， and if the currents associated with these

waves are superimposed upon the ordinary tidal

currents (8verdrup， Johnson and Fleming， (1965の)).

At first glance it may appear hopeless to separate

the later from the currents of the internal waves of

tidal periods， but fortunately these “internal tidal

currents" can be eliminated if observations are

available from a sufficient number of depth.

Because

δηn vn = Cnーでごー一 ， 。z

、、，ノ1i

〆，‘、

Where vn is the horizontal water velocity of the

wave of nth order， and and cn and the corresponding

velocity of progress and vertical displacement ; and

because for all internal wavesηis zero at the surface

and at the bottom， one has generally

υぐCn円 ， (2)

It f10ws from equation (2) that currents associated

with internal waves are eliminated by computing

the average currents between the surface and the

bottom， provided that observations from a sufficient

number of depths are available (Defant (1932の)).

Internal tida1 waves are beroclinic and are consid-

ered to have a significant effect on mixing in the

ocean. The internal tidal waves have characteristic

tidal periods and wavelengths of the order of hundreds

2.2 Observations of internal tidal waves

It is not easy to discriminate the water motion

generated by internal waves from tidal current by

observation in the open sea as well as in a bay. The

water motion due to internal waves could be recog-

nized only at a locality like the inlet of the inner-

most part of a bay where it is ordinarily calm

10 JAMSTECR， 35 (1997)

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11

The variations of currents and isotherms at the bottom and the surface layers compared

JAMSTECR， 35 (1997)

Fig.2

3 Water motions associated with internal waves

3.1 Horizontal water motions

It is well known that a current generates sand

ripples on the sea bottom， and various investigations

of this phenomenon have been made. It is thought

that in shallow water sand ripples are generated by

the movement of water associated with surface

waves， and in a deeper water by a current. It is also

known that sand ripples exist on the sea bottom

even at depths of several hundred meters or more.

LaFond (196p2)) studied the water motion caused by

internal waves in shallow water by means of vertical

strings of thermistor beads and of an isotherm

flower， and revealed the effect of sediment moving

current created by a horizontal motion set up by

internal waves.

Jacobsen and Thomson(193413)) observed that the

currents and the water motion generated by the inter-

nal tidal waves weaken or strengthen each other in

the Strain of Gibraltar. The water motion generated

by internal tidal waves having large amplitude has

the greatest effect on the tidal current through super-

position. It seems that the effect of the sediment

transportation also becomes great when the internal

tidal waves break at the steep sea floor.

3.2 Movement of the bottom sediments

ln coastal stratified areas， since the pycnocline is

stable， the large kinetic energy from the upper layer

can be transported to the deeper water through the

wave motion of pycnocline. On stormy days， the

pycnocline is still maintained in the stable stratified

area， and the internal wave height becomes larger，

so the effect of internal waves on sediments becomes

greater.

The water motion generated by internal tidal

waves having large amplitude also has a great effect

on the tidal current through superposition. It seems

that the effect of sediment transportation becomes

great when the internal tidal waves break at the

steep sea floor (Midorikawa (1995aω)， Midor比awa

and Sakakida (1996a2>)).

The horizontal motion caused by internal waves

below the trough becomes stronger as the thermocline

12

approaches the sea bottom. The values of the horizon-

tal motion are estimated for various thicknesses of

the lower layer.

Interesting features of big scale ripples were recog-

nized on the hard bottom and sediments of several

centimeters in diameter were scoured at the trough

of the ripples. The distances between the troughs were

about 1.8 meters and the trough (or crests) extended

more than 300 meters parallel to each other

(Midorikawa (19751)， 1976bベ1995a's>)and Photo. 4).

It has not been clarified whether internal waves were

a cause of the big scale ripples or not in those

days.

We made sure that the horizontal motions caused

by tides or internal tides were over 1 knot near the

deep bottom， and sediments of sand and stones on the

sea floor were scoured by strong current(Midorikawa

and Matsumoto (1986ω)， Midorikawa， Momma，

Mistuzawa and Hotta (19881η )， Midorikawa (1995aω

)). Besides， the thermocline in the area was not

been destroyed even in the middle of strong storms

(Midorikawa (1976b14))).

3.3 Thermocline in the ocean

A thermocline is a layer of sea water with a

greater vertical gradient in temperature than that

reside in the layers above and below it. The boundaries

of this height grandient layer form the division of

the surface water and the intermediate water

below.

Thermoclines can be affected by physical processes

and meteorological processes occurring in the oceans.

1n general， two major types of thermoclines may be

indentified， namely， the permanent thermocline and

the seasonal thermocline. The permanent thermocline

is unchanged seasonally and is generally the deeper

thermocline to be found at a depth of several hundred

meters below the surface， and which are generally

thought to be developed by the equator ward flow

of deeper water from the poles and the poleward

flow of warm surface water from the equater.

Seasonal thermocIines are found nearer the surface

than the permanent thermocline and in those areas

where the seasons show noticeable differences from

JAMSTECR， 35 (1997)

T EMPERATURE (OC)

2 0 2 I 2 2 2 J 2 4 2 5 20 2 I 2 2 2 3 2 4 2 5 0

10 ，嗣、、

.520 工トー

<l...

包:30 r- 「40 l- グ/ ド

Fig. 3 The vertical distributions of temperature of single measurements on September 25 (left) and

28 (right).

Photo 4 Ripple marks and erosion which occurred by the strong current on the sea floor at a

depth of 2，OOOm at the mouth of Suruga Bay.

Photo 5 Big scale ripples formed on the hard bottom

observed neεr the front of coaotal area.

JAMSTECR， 35 (1997)

summer to win:er. As air temperatures rise above sea

temperatures in the spring and the surface water

receives more beat than it loses by radiation and

becomes warmer. The wind then acts to cause mixing

of the surface water. The wind continues to mix the

ourface mixing layer deeper， the thermocline 1ayer

will become further below the surface.

Thermoclines have various effects， such as the

contribution to the sediment transport by water

movement associated with internal waves or the

transmission of sound. If a thermal boundary is

near a floor， the flow speed under the trough is

increased. But it is thought that then the Internal

wave trough comes closer to the bottom， they become

flat and broad by the conflict of the current through

the constriction between the trough and sea floor as

seen in tbe left panel of the figure， so the current

strength is reduced (Fig. 1 ).

The structure of the thermocline is infl uenced by

the changes of seasons as mentioned above. For ex-

ample， in shallow water areas， a strong thermocline

appeared at 50me meters above the bottom， and it

almo5t vanished and the sea water became more or

less homogeneous owing to the turbulent mixing

after three days (Fig. 3 ).

4 Considerations

When an internal thermal boundary is near the

sea floor， the f:ow speed under the trough is Increased.

So the maximum turbulence will be under the trough，

but main speed will be in the direction opposite of

wave propagation (Midorikawa and Sakakida (1996

a2)). Midorikawa (1975り).In coastal areas， the in-

ternal wave direction is foward the shore， thus the

maximum speed near the bottom wil1 be offshore.

The flow caused by tidal or internal tidal motions

sometimes transport shelf sediments at the depth

of several hundred meters or more (Photo 4 ，

Midoriko.wa et 0.1 (19861

へ198811))).

It was found that slight water movement of the

intermediate layer was sensed near the bottom by

diving fisbermen and women when we cannot sense

inconsiderable fluctuations on the sea surface. On

the contrary， water movement is strong enough to

13

dislodge big stones on the sea bottom when stormy

weather approaches.

In continental shelf areas， when the pycnocline is

stable and deep， large kinetic energy， like from a

typhoon can be transported from the upper layer to

deeper water through the wave motions of thermal

boundary (Photo 5， Midorikawa (1995aIS))).

The water motions generated by internal waves

having large amplitude， just as internal tidal waves，

have a great effect on sediment transportation

when internal waves break at the shelf floor as seen

in Fig. 1 . Even in deep water， the water funneling

associated with internal wave motions through the

constriction caused by the trough and bottom is a

contributor to the offshore movement of sediments.

14

References

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Bay， Internal wave-motion and marine sedi-

memts. The 3rd International Ocean Develop-

ment Conference， preprint vo1.V， 11-20. (1975)

2) Midorikawa， K. & N. Sakakida : On Internal

Waves in a TwかLayerOcean ( 1 )， vo 1.33， 1-5.

(l996a)

3) Midorikawa， K. and T. Miyazaki: Observations

of Internal Wave Velocities. JAMSTECR 1，

109-114. (1977a)

4) Midorikawa， K : The Effect of Tidal Currents

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5) Midorikawa， K ; On Internal Waves in Suruga

Bay. J. Fac. Mal. Sci. Technol， Tokai Unniv.

Spec. 'No. 1・74.(1977c)

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Bull. Coastal Oceanogr・.101-105. (1973b)

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period internal waves， JAMSTECR， 34， 25・29.

(1996c)

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9) Sverdrup， H. U.， M. W. Jonson and R. H.

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University Press， 61-77. (1934)

13) JACOBSEN and THOMSON : in Physical

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Pergamon Press， (1934)

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Current and Marine Sediments. Bull. Coastal

Oceanogr・.13 (1)， (1976b)

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Curren t -. J AMSTECR Deep-sea Research，

107-113， (1986)

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and H. Hotta， : Meassurment of the Deep-sea

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109. (1988)

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(原稿受理:1996年12月5日〉

JAMSTECR， 35 (1997)