Physical Oceanography

Lecture 2: 5/29/2014

Quiz 1

• Emailing now …

Back to the basics

• Important factors influencing water:– Temperature• Water has high heat capacity

– Salinity• Gradient Freshwater Brackish Marine

– Freshwater still has some salts– It takes a lot of effort to deionize water!

– Pressure (minor, and won’t be discussed)– All the above affect water density

Water’s heat capacity:• Water:

– Solidliquid– Liquidgas – Both require energy to break

bonds (e.g. van der Waals forces, hydrogen bonds)

• Extra energy required o break H bonds causes freezing & boiling points to be anomalously high– Not unique to water (see

other H-bond molecules)

Water’s heat capacity:• The hydrogen bondA) molecules in the ice crystal lattice

– Very open, results in low ice density

B) clustered water molecule (no H bonds shown)

– More likely to form & persist longer at low temperatures

– Reason water’s density decreases <3.98C

C) unclustered water molecule (no H bonds shown)

Water’s heat capacity:

Importance: high heat capacity allows large amounts of heat energy to be stored in ocean

without much temperature change heat-buffering capacity for climate

Water density: Temperature

Density of pure water plotted against temperature

Water density: Salinity

The relationship of salinity (30 to 40 PSU) to density at fixed temperature

The relationships among salinity, temperature, and density

Water density: Salinity

Increasing salinity reduces both the freezing point.

Water can layer

(a)Water is stably stratified and no water sinks or rises. (b)If water is introduced, it sinks/rise until it reaches an equilibrium level

(density of the water above it is lower and the density of the water below it is higher). It will then spread out to form a new layer at this depth.

What about mixing? … - Some mixing will occur as it sinks through layers. - Vertically moving water masses are very large in the oceans, mixing is

limited.

The “coffee” ocean

Mixing can occur via molecular diffusion or physical processes:- If you let molecular diffusion mix your cup of coffee, it would take a

couple of weeks (maybe even months depending on where you introduce the cream).

- Physical mixing is much quicker, but requires input energy (i.e. work)!

Ocean water movement

• Typically broken down into three categories:– Short time scales (mostly seconds to hours)

1) Waves2) Tides

– Most dynamic time scale (seconds to centuries)3) Ocean circulation

How to make a surface wave?

• For surface water waves to occur, need:– a disturbance (source)– a restoring force– a medium for the energy to travel away from the

source• Eventually, damping or dissipation will stop the

energy transfer somewhere.• The ocean is a medium for a wide variety of waves

with different sources and restoring forces.

Ocean Surface Waves• Disturbance: sea surface is displaced

– Winds– vertical displacement– produce pressure disturbance

• Restoring Force:– Gravity– surface tension– Earth’s rotation

• Propagation:– pressure gradients due to different water heights

• Dissipation:– bottom friction– wave breaking

Wave terminology• Crest & Trough:

– Lowest and highest points, respectively

• Height (H): – Vertical distance between crest and

trough• Amplitude (A):

– Half of height• Wavelength (L):

– Distance between adjacent wave crests

• Period (T)– Time between two crests at a fixed

point

Wave/water motion

• A wave transfers energy from point to point

• A wave form travels with the wave (propagates), but the water does not (i.e. bird’s starting/ending position the same)

A little math (see terminology slide)

• Wave (Phase) speed (c): c = L / T• Wave Speed and Dispersion relation– Equations of motion• equates c to water depth (d) and wavelength (L):• g = 9.81 m/s2 (gravity)

– Complicated but valid for all water depths

Deep water vs. Shallow water Dispersion

• Deep water:– Good for water depth, d > L/2– Longer waves travel faster (dispersive)– Depth, d not important to c

• Shallow water– Good for d < L/20– C does not depend on wavelength so all wavelengths

travel as the same speed (non-dispersive)

Motion of deep-water vs. shallow-water waves

• Deep water– Circular paths– Shrink exponentially with depth– Crests move with wave

direction– Troughs move against– Wave motion essentially zero at

depth L/2• Shallow water

– More along-wave motion than vertical

– More flattened toward the bottom

Swell Propagation in Deep Water

• Within the fetch of a storm the waves are irregular because they are the sum of many separate waves of different wavelengths

• Long-wavelength waves move faster than shorter-wavelength waves and move ahead (sorting by wavelength “wave dispersion”)

• Waves appear to become smoother as they travel out from the storm fetch.

Wave shoaling• Water depth decreases toward shore• Waves slow down• Wave length, L, decreases (period, T, does not)• Energy flow is nearly conserved; therefore, wave height, H, increases

– tsunami in open water has large L, but small H; this changes when it feels the bottom

• When water at top of wave moves faster than wave can travel breaks (surf zone)

Wave Energy Extraction

• Not a trivial amount of energy:• A “big wave” Example:

– Deep water wave, H = 2m, T = 10 s– L = 156 m (deep water), c = 15.6 m/s (deep water)– Energy = 5000 J/m2

– Power = 1.6x1010 W = 16 GW (16,000,000 kW)• Average annual US Household electricity consumption per year?

11000 kWh or 1.25 kW• This one wave could power 12,800,000 households for a year• Equivalent gallons needed for this much energy?

– Gasoline: 456,000 gallons– Natural gas: 2,267,000 pounds

Other types of waves in ocean

• Internal waves:

• Kelvin waves:– Large scale surface & internal waves• Wavelengths (100 to >1000 km)• Periods (days to months)

– Example: El Niño/La Niña• Tides!

What are tides important? Ships

Please don’t

hit me!

Safety • Tidal Bores– tide wave that moves very fast– they are dangerous– only occur in some parts of the world

Tidal Bore, Truro, Nova Scotia

• Why care?–Real estate–Tidal currents•Moves things (pollutants, organisms)•Mixes water• Important to estuarine exchange

Tides vary by location

• Mobile Bay … only one small tide per day

• Daily & semi-daily frequencies (F on graph is relative strength of seim-daily & daily frequencies)

• Longer period modulations (e.g. weekly)

Equilibrium Tide Theory• Origins with Newton• Oversimplification:

– Earth is sphere covered with water to uniform depth– No continents– Ignores effects of friction– Rotation: earth & moon around common center of mass– Gravity: effects among earth, moon, sun

• Key forces:– Gravity: attracts all parts of Earth/moon to each others center– Centripetal force: (NOT centrifugal) revolution of earth/moon

around common center of gravity

• Total gravitational force (between Earth & moon or sun) must = total centripetal force (maintains two bodies in common orbit). • Centripetal force is the same at all points on earth• Gravitational force varies slightly at different points

• On the side of the Earth nearest the moon, the gravitational force due to the moon is slightly higher than it is at the Earth’s center. • Closest to moon: gravitational force > centripetal force • Directly away from moon: centripetal force > gravitational force • Pressure gradient (i.e. tide-generating force) compensates at both

Horizontal tidal forces. (a)As in last slide, but varies by latitude, note where tidal force goes to

zero (b)Tidal force = zero in a ring (annulus) around the Earth that is

equidistant from these two points (under moon, directly opposite).

• Tide bulges caused by the moon’s tidal forces and change with declination

• Moon is “overhead” at any point on Earth a little later each day, makes diurnal inequality• A - diurnal tide• B - semidiurnal tide• C and D - mixed tides.

Spring and Neap tides• A simplified depiction of the Earth–

moon–sun system shows how the solar and lunar tides interact to create spring and neap tides.

(a) Full Moon: Spring tides – greater tidal range– moon and sun’s bulges aligned, maxima

at same locations (b) Third-quarter Moon: Neap tides

– moon & sun’s bulge aligned at 90° – maxima of moon’s tide & minima of

sun’s tide. (c) New Moon: Spring tides

– moon and sun’s bulges aligned, maxima at same locations

(d) First-quarter Moon: Neap tides – moon & sun’s bulge aligned at 90° – the maxima of the moon’s tide coincide

with the minima of the sun’s tide.

Equilibrium theory poor at predicting tides

Dynamic Tide Theory Considers:• Continents restrict flow to basins (e.g. Pacific, Atlantic)• Coriolis force (effect of earth’s rotation) causes water in steady motion

to veer right (N. hemisphere) or left (S. hemisphere) … more later• Thus, instead of tides sloshing back/forth in a basin, they slosh

AROUND the basin

Amphidrome: Wave + Basin + Rotation

Example: a broad basin• Dashed lines =

amplitude (increases away from amphidrome)

• Solid lines denote position of wave crest at any one time• Is a “Kelvin wave” –

it travels along coast and decays out to sea, if basin wide enough it forms amphidromic system

Amphidromic systems of the principal lunar semidiurnal tidal component. Lines = tidal maximum; numbers hours that elapse as the tide crest travels from the line labeled 0.

Ocean Circulation

• Two main temporal scales– Slow (Centuries)• Thermohaline circulation• Driven by latitudinal variations in water density (i.e.

deep water formation)– Rapid (days to year)• surface currents• Driven by wind, Coriolis and pressure gradients

Meridional Overturning Circulation (aka Thermohaline Circulation)

• Starts with the formation of North Atlantic Deep Water near Greenland.

• Flows south & mixes with the deep water formed near Antarctica

• Transported around Antarctica, into the Indian and Pacific Oceans (ventilates to surface in many regions, e.g. north Pacific)

• MOC creates water mass layers (Atlantic below)

• MOC creates water mass layers (figure from Hansell 2013)

Surface Currents (wind, pressure gradient, Coriolis)

Coriolis Force

• In non-rotating frame of reference– Particle moves at constant speed & straight line

unless acted on by a FORCE• In rotating frame of reference– Same particle viewed from rotating frame the path

appears curved

Ekman Transport• The Ekman spiral: – Coriolis deflects water to

right (N. hemi), left (S. hemi)

– kinetic energy is transferred downward in the water column

– each layer of water is deflected to the right of the direction of the layer above

– produces spiraling current – Net 90 degree transport

• Pressure Gradient– Coriolis deflects water 90

degrees to right (N. hemi)– Slopes sea surface to

create pressure gradient• Flow direction

– Pressure > Coriolis?– Coriolis > Pressure– Pressure = Coriolis

• Geostrophy!• Arrow diagrams (bottom)

Tying things together:- Wind- Coriolis/Ekman- Pressure gradient

HOMEWORK

• Reading 2 (see Sharepoint)• Next Time:– Lab 1a due (THIS IS DIFFERENT FROM SYLLABUS)– Morning:

• Quiz on Reading 2• Lecture topics:

– Chemical oceanography– Geological oceanography

– Lab activities:• Preparation for field trip on Monday

– Introduction to sampling methods