EES215

Lecture 15

 

Interaction of wind with surface waters:  velocity u of current resulting from wind with speed w:

uo = t/Ö(Azrf),
t = c w2,

with c, a function of wind speed and flow conditions, being between 1 and 10 x 10-3 kg/m3
Az = ~102 kg/m-s (vertical eddy viscosity)
The resulting current is deflected by the Coriolis Force by about 45ocum sole; deeper layers are continuously deflected, move slower and form the Ekman Spiral.

Winds are distributed in specific zones:  Fig. 1
 

Pressure gradient - geostrophic movement
Ocean has limits => horizontal pressure gradients result

Hydrostatic pressure at depth z: p = mg = Vrg; for unit area p = rg z
Horizontal pressure gradients occur when height of water or density changes laterally, driven by the pressure gradient force PGF (Fig. 2)
At two locations A,B with height of water columns z; z+Dz:

pA = rg z; pB = rg (z+ Dz)

Horizontal pressure gradient: Dp/Dx = rg tan q; with q the angle between the surface and the isobare between A and B.
The velocity of the resulting current is

u = (g/f) tan q.

 

Slope of isobars between stations A and B, separated by distance L, with heights hA and hB above reference level:

tan q = (hB – hA)/L

and

u = (g/f)/ ((hB – hA)/L)

 

Difference in hydrostatic pressure between isobars is the same in A and B, i.e. differences are reflected in densities:

rA g hA = rB g hB à  hA = hB (rB /rA)

and

u = ghB (1- rB /rA)/(f L)

i.e. the geostrophic velocity at any depth can be calculated as a function of density variations between two stations.  The direction of the resulting current is determined by the equilibrium between pressure gradient force (PGF) and Coriolis Force (CF).

 

Water moves from high to low pressure - as it moves CF changes direction of movement until PGF and CF are equal, movement in right angels to pressure gradient.
 

Geostrophic currents:
Pressure driven currents - the influence of sea floor topography and presence of shores; horizontal pressure gradient - balance between horizontal pressure gradient force and Coriolis force: current is in geostrophic equilibrium: geostrophic current. Cause for horizontal pressure gradient: influence of slope in sea floor on surface of ocean

Barotropic condition:  isobaric surfaces are parallel to surface and to isopycnic surfaces (equal density): hydrostatic pressure controlled only by slope of sea surface baroclinic condition: isopycnic surfaces and isobaric surfaces not parallel (Fig. 3)

Currents in response to pressure gradients move down the pressure gradient but are subject to Coriolis force - deviate in right angle to initial motion (Fig. 4)
 

Gulf Stream
Wind field N of 30o to the east, south to the west - resulting current wind driven + Coriolis force - diagram
Current due to Ekman transport and geostrophic flow due to 'piling up' on coast of Africa
Result if two coast lines are taken into account – Fig. 5
Actual distribution of Gulf Stream (Fig. 6)
 

Three dimensional movement related to distribution of salinity and temperature: Thermohaline convection.
Salinity is amount of salt in solution, measured in permille; example for salinity variations: Strait of Gibraltar (Fig. 7)

Changes in temperature and salinity result in a world-wide transport of water. The main sink of cold water at present is in the North Atlantic, with smaller amounts formed in the Weddell Sea (Antarctica). This ‘conveyor belt’ is crucial for the thermal balance of the oceans and the atmosphere (Fig. 8)

The amount of water in the thermohaline convection is estimated to be 15 Sv (1 Sv = 106m3/s)

Energy considerations:

Energy in ‘conveyor belt’:

E = m DT cW

DT temperature difference (~ 3 deg) between starting and ending condition; cW heat capacity of water (4.17x103 J/kg-deg)

With these figures, the total energy in the ‘conveyor belt’ is 1.875x1014 W

Comparison:

            Solar energy flux at top of atmosphere:              1.7x1017 W

            Geothermal energy flux:                                     3.2x1013 W

            Tidal                                                                 7.0x1012 W

            Human energy consumption rate:                       1.2x1013 W

 

Tsunamis: Interaction between lithosphere and hydrosphere: The sudden vertical movement caused by a large earth quake produces a wave which will travel from its source in all directions.  Fig. 9

Tsunami waves have typically very large wave lengths (> 100 km) and travel a great speed over the open ocean.  The velocity can be approximated to

c=        Ö(gd)   with g gravitational acceleration and d water depth

Energy in waves depends on the wave height H

E = 1/8 r g H2  [J/m2]

Wave height is not easily related to wave velocity and period and typically must be observed.

A very large Tsunami was caused by an earth quake in the Sumatra Trench on 26 Dec., 2004.  While wave heights over the open ocean typically are > 1 m, as waves reach coastal areas, wave heights increase dramatically, since the energy of the wave remains largely the same.  In the Sumatra Tsunami, wave heights of more than 30 m were observed.  The Tsunami reached also coasts in Thailand, Sri Lanka, India and East Africa (Fig. 10; see animation in the NOAA website) and caused the deaths of more than 200,000 people.