Physical Oceanography

1. What drives the ocean currents?

If we exclude tidal forces, the oceanic circulation is driven by four external influences:

- rotation of the Earth;
- wind stress;
- heating and cooling;
- evaporation and precipitation.

The last three are ultimately driven by radiation from the sun.

The solar heating is unevenand at different latitudes: more sunlight falls in equatorial regions than strikes the poles (This and many other illustration in this lecture were taken from the book written by Tom Garrison, "Oceanography: An Invitation to Marine Science", Wadsworth Publishing Company, Belmont, 1993, 540 pp. Figure 8.2).

Warm air rises and cool air sinks; a convection current forms in a room resulting from uneven heating and cooling (Garrison, 1993, Figure 8.3).

(Garrison, 1993, Figure 8.4).

The amount of heat radiation is of maximum at the equator. The cold air at the poles is denser than the warm air at the equator; hence, air pressure at sea level is higher at the poles than at the equator. In other words, the pressure gradient at sea level is directed from the poles toward the equator, and the pressure gradient in the upper part of the atmosphere has the opposite sign.
In fluid and gases pressure gradients produce flow from regions of high pressure to regions of low pressure. If the earth were not rotating, the response to these pressure gradients would be direct and simple.

(Garrison, 1993; Figure 8.5).

At the higher latitude each location travels a shorter path on the rotating Earth than at the equator.

(Garrison, 1993; Figure 8.7).

A cannonball shot north from the cannon located at the equator is also moving east at the speed of the Earth rotation at the equator and veers to the right from its northward path.

A cannonball shot south travels over portions of the Earth that are moving increasingly faster in an eastward direction and also veers to the right.

This effect is called “Coriolis effect”.

(Garrison, 1993; Figure 8.9).

The rotation of the Earth modifies the pattern of atmospheric circulation in two ways. Firstly, as air moves toward the equator, the rotation of the earth shifts ocean and land eastward under it. The result is "easterly" winds (Polar Easterlies and Trade winds).

Secondly, the zonal flow of high speed becomes unstable, creating eddies which reshape air pressure distribution resulting in air pressure maximum in mid-latitudes. It creates a band of "westerly" wind in the Roaring Forties.

At this animated image you can see the seasonal variations of wind over the World Ocean averaged during several decades of observations.

(Garrison, 1993; Figure 8.13).

In coastal zones the atmospheric circulation pattern is modulated by the difference between the heat balance over land and sea zones.

During summer land accepts more heat and onshore wind dominates.

During winter land is cooler than sea and offshore wind dominates.

1.2. Wind stress

Wind stress t (kg m^-1 s^-2 or Newton per m²) is an important quantity in the process of wind driving ocean currents.

where

C_d is the dimensionless "drag coefficient" (about 0.0013),

is air density (about 1.2 kg m^-2),

U is wind speed at 10 m above sea level (m s^-1).

Wind stress is a square function of wind speed because the wind forcing depends on wind speed and sea roughness, which in turn depends on wind speed.

2. The heat flux through the ocean surface

The heat flux is determined by the balance between four components:

200 W m^-2 warm a layer of water 50 m deep by about 2.5°C per month if unopposed by heat losses from other effects.

Annual mean solar radiation (W m^-2) received at sea level (Illustration from the book written by Matthias Tomczak and J. Stuart Godfrey "Regional Oceanography: An Introduction", Pergamon Press, Oxford, 1994, 414 pp.; Figure 1.5).

Annual mean heat flux into the ocean depends on solar radiation and sea surface temperatur (Tomczak and Godfrey, 1994; Figure 1.6).

Sea surface temperature in degrees Celsius during Northern Hemisphere winter (Garrison, 1993; Figure 7.20).

3. Vertical distribution of water properties

(Garrison, 1993; Figure 7.11).

Pressure p (kiloPascal, 10 kPa = 1 dbar = 1 m);
Temperature T (degrees C);
Salinity S (Practical Salinity Units - psu) correspond to promille (g salt/kg sea water);

Density (kg m^-3) represented by

(Garrison, 1993; Figure 7.8).

The equation of state indicates that water density is a function of temperature, salinity, and pressure.

The pressure field
The pressure in the water column increases with depth and depends on the vertical distribution of water density. We can calculate differences between pressures at different depths or depth differences between two surfaces of constant pressure. For the latter purpose a quantity called steric height is introduced.

Its meaning is the height by which the water column between depths z₁ and z₂ with standard temperature T = 0°C and salinity S = 35.0 expands if its temperature and salinity are changed to the observed values.

Typically h is a few tens of centimeters. Oceanographers map the shape of the sea surface by showing contours of equal steric height relative to a depth of no motion, where pressure is assumed to be constant (usually 1500 or 2000 m).

Dynamic height D (m2 s^-2) is equal to g * h, i. e., the product of gravity and steric height.

From steric height or dynamic height we can estimate the horizontal pressure gradient resulting in geostrophic water circulation.

4. Water circulation

4.1. Horizontal circulation

Mass transport and volume transport

Mass transport is the transport of water through an area of unit width (1 m²), units (kg m^-2 s^-1).

Volume transport is a mass transport integrated over the width and depth of a current, divided by density. Units are m³ s^-1 or Sverdrup (Sv), 1 Sv = 10⁶ m³ s^-1.

Geostrophic flow

Distribution of isobars and isopycnals at any depth level
above z = z₀ (Tomczak and Godfrey, 1994; Figure 2.7).

Water at station A is denser than water at station B. As the weight of the water above z = z₀ is the same, the water column must be longer at B than at A.

In geostrophic flow, water moves along isobars, with the higher pressure on its right in the Northern Hemisphere (away from the equator).

The magnitude (mass transport per unit depth) of geostrophic flow:

where is an average water density,
g is acceleration of gravity (g = 9.8 m s^-2),
T_d is the length of a day (86,400 s),
is the latitude,
is the difference in steric height between two adjacent isobars.
is known as Coriolis parameter.

Mean dynamic height (m² s^-2), or steric height multiplied by gravity, for the World Ocean at 0 m relative to 2000 m. Arrows indicate the direction of the implied geostrophic movement of water (Tomczak and Godfrey, 1994; Figure 2.8).

Illustration of the relationship between a map of steric height (dynamic topography), geostrophic flow, and the evaluation of the geostrophic mass transport per unit depth M' between two streamlines (contours of constant steric height) in the Southern Hemisphere (Tomczak and Godfrey, 1994; Figure 3.2).

For both station pairs, A and B and A' and B', in Equation is given by h₂ - h₁.
The geostrophic velocity is inversely proportional to the distance between streamlines, or equal to M' divided by density and by the distance between points A and B, because the section AB is perpendicular to the streamlines.
If station pair A' and B' is used for the calculation, similar Equation still produces the correct geostrophic mass transport M' between streamlines h₁ and h₂, but the velocity derived from M' and distance A'B' is only the velocity component V_n perpendicular to the section A'B'.

1½-layer model

Side view of a 1½-layer ocean (Tomczak and Godfrey, 1994; Figure 3.3).

1½-layer model is is an approximation to the ocean's density structure. The ocean is divided into a deep layer of constant density r2 and much shallower layer above it, again of constant density The lower layer is considered motionless. The thickness of the upper layer z = H(x, y, t) is allowed to vary.

The factor is of the order 0.01 or less. Hence, in a 1¹/₂ layer ocean the sea surface is a scaled mirror of the depth of the pycnocline (100-300 times larger).

Rossby wave in the Southern Hemisphere (Tomczak and Godfrey, 1994; Figure 3.4).

Total poleward flow in greater in magnitude between A and B than between C and D because the Coriolos force f is smaller in magnitude at A and B than at C and D; the thermocline deepens in ABCD. By the same argument, the thermocline shallows in A'B'C'D'; the eddy moves west.

The direction of circulation in the eddy structures is important.
In the Northern Hemisphere, the eddies with cold core are rotating counter-clockwise.
In the Southern Hemisphere, these eddies are rotating clockwise.
In both cases, this type of rotation is called cyclonic.

The eddies with warm core are rotating clockwise in the Northern Hemisphere and counter-clockwise in the Southern Hemisphere.
These eddies are called anticyclonic.

Ekman drift

The Ekman spiral and the mechanism by which it operates. (a) The Ekman spiral model. (b) A body of water can be thought as a set of layers. The top layer is driven forward by the wind, and each layer below is moved by friction. Each succeeding layer moves at a slower speed, and at an angle to the layer immediately above it (to the right in the Northern Hemisphere, to the left in the Southern Hemisphere) until friction becomes negligible. (c) Though the direction of movement is different for each layer in the stack, the theoretical average direction of flow of water in the Northern Hemisphere is 90° to the right of the prevailing surface wind (Garrison, 1993; Figure 9.5).

The movement of water away from point B is influenced by the Coriolis effect and gravity (Garrison, 1993; Figure 9.6).

The current moves at an angle to the wind (to right in the Northern Hemisphere), turning further away from the wind direction and becoming weaker with depth. Therefore, the wind-driven component of water transport is directed perpendicular to the mean wind stress to the right in the Northern Hemisphere. The magnitude (kg m^-1 s^-1) is

where is wind stress and f is Coriolis force.

The combination of geostrophic flow and wind forcing results in the general pattern of ocean currents (Garrison, 1993; Figure 9.8).

The general circulation in all oceans is anticyclonic, i.e., clockwise in the Northern Hemisphere and counterclockwise in the Southern Hemisphere (Garrison, 1993; Figure 9.2).

4.2. Vertical circulation