## Seasurface slope and the geostrophic current

It may seem a little fantastical that the wind can produce a change in the sea level and that this in turn can produce the currents of the great gyres. However, we do not need a large change in the sea level to produce quite substantial flows, as we can see with a simple calculation. The geostrophic current is a balance between the Coriolis and pressure gradient forces, so that fu -12P fv ± . (4.1a, b)

The pressure at a level below the surface is given by the weight of the fluid above it, so that p = pgh, (4.2)

where h is the height of the column of seawater and p is the density of the seawater. Thus, using equation 4.2 in equation 4.1a and b, we get fu g% fv g2t. (43a, b)

Suppose that the height of the sea surface varies by just 1 m over a horizontal distance of 1,000 km—a truly small slope that would be extremely difficult to detect by measurements of the ocean surface but that is, remarkably, measurable using modern satellites. The magnitude of the currents produced is then given by u = =-j —7. 0.1ms1. (4.4)

Such a current is easily measurable, and when one considers that billions of tons of water might be put in motion this way, one begins to see the large effect that this current can have.