Chapter 10  Geostrophic Currents 10.1 Hydrostatic Equilibrium Within the ocean's interior away from the top and bottom Ekman layers, for horizontal distances exceeding a few tens of kilometers, and for times exceeding a few days, horizontal pressure gradients in the ocean almost exactly balance the Coriolis force resulting from horizontal currents. This balance is known as the geostrophic balance. The dominant forces acting in the vertical are the vertical pressure gradient and the weight of the water. The two balance within a few parts per million. Thus pressure at any point in the water column is due almost entirely to the weight of the water in the column above the point. The dominant forces in the horizontal are the pressure gradient and the Coriolis force. They balance within a few parts per thousand over large distances and times (See Box).
Both balances require that viscosity and nonlinear terms in the equations of motion be negligible. Is this reasonable? Consider viscosity. We know that a row boat weighing a hundred kilograms will coast for maybe ten meters after the rower stops. A super tanker moving at the speed of a rowboat may coast for kilometers. It seems reasonable, therefore that a cubic kilometer of water weighing 10^{15}kg would coast for perhaps a day before slowing to a stop. And oceanic mesoscale eddies contain perhaps 1000 cubic kilometers of water. Hence, our intuition may lead us to conclude that neglect of viscosity is reasonable. Of course, intuition can be wrong, and we need to refer back to scaling arguments. 10.1 Hydrostatic Equilibrium
the fluid remains stationary:
and, there is no friction:
With these assumptions the momentum equation (7.12) becomes:
where we have explicitly noted that gravity g is a function of latitude φ and height z. We will show later why we have kept this explicit. Equations (10.4a) require surfaces of constant pressure to be level surface. A surface of constant pressure is an isobaric surface. The last equation can be integrated to obtain the pressure at any depth h. Recalling that r is a function of depth for an ocean at rest.
For many purposes, g and ρ are constant, and p = g h ρ. Later, we will show that (10.5) applies with an accuracy of about one part per million even if the ocean is not at rest. The SI unit for pressure is the pascal (Pa). A bar is another unit of pressure. One bar is exactly 10^{5 }Pa (Table 10.1). Because the depth in meters and pressure in decibars are almost the same numerically, oceanographers prefer to state pressure in decibars.


Department of Oceanography, Texas A&M University Robert H. Stewart, stewart@ocean.tamu.edu All contents copyright © 2005 Robert H. Stewart, All rights reserved Updated on October 8, 2007 