EES215

Lecture 14

Thermodynamic forces: energy flux: solar radiation; geothermal flux; temperature distribution in the ocean:  Fig. 1
Thermocline; dependence on latitude and season:  Fig. 2
latitudinal differences in solar radiation; extent of ice caps; formation of cold bottom water; stratification of the oceans (gravitation)  Fig. 3
Transport of energy from low to high latitudes, cause for ocean currents and wind patterns  Fig. 4

Rotational forces: definition of the Coriolis effect - apparent force.  Fig. 5
Coriolis force (CF) acts at right angles to the direction of motion, causing deviation to the right in northern hemisphere, to the left in southern hemisphere.
CF increases from zero at equator to maximum at poles.

CF = m 2 W sin(f) u

with m - mass, W - angular velocity 7.29x10^-5 s^-1, f - latitude, u - velocity.

Coriolis parameter,  f = 2 W sin(f)

CF = m f u

Formation of currents - transport of energy from equator to polar regions (graph)

Surface currents: interaction of wind with oceans - force distribution; energy transfer from wind to surface layer of oceans - gravity waves; currents; frictional force between wind and surface layer of ocean: wind stress = cW² (W wind velocity)
c depends on atmospheric conditions: the more turbulent convection in atmosphere the higher is c; (c 2x10^-3)

Frictional coupling between layers of ocean: laminar motion - transfer of momentum between adjoining molecules - molecular viscosity; turbulent motion - transfer of momentum betwen parcels of fluid - eddy viscosity; at surface of ocean always turbulent motion; Eddy viscosity A: two components: horizontal mixing 10⁴ -10⁸ kg/m-sec; vertical lower by several orders of magnitude: different rates of mixing in horizontal and vertical directions.

Ekman spiral Fig. 6

Wind induced current: Ekman Spiral: three forces at work: stress of overlying water (wind at surface); stress of underlying water, and Coriolis Force. => current deviates increasingly cum sole with increasing depth. Surface current deviates by 45^o from wind direction; speed of current decreases exponentially with depth as well as turning further cum sole until at depth D it has 4% of surface velocity and is exactly opposite of surface direction. (Theoretical derivation, friction and other considerations change situation)

Inertia currents:  Fig. 7

When winds stops, water continues to move (low friction). Active forces: Coriolis Force = centripetal force

m f u = mu²/r  =>   f = u/r

Water will follow circular path with radius r at constant speed u.
The time taken for a water parcel to complete one circuit is called the period of inertia current

T = 2p/f

Since f is function of latitude, T decreases from equator to poles.