## W

Cono lis torce

Corioiis force t pressure gradienl force initial situai ion

(bi PLAN

Figure 3.12 (a) A sea-surface slope up towards the east results in a horizontal pressure gradient force towards the west, (b) Initially, this causes motion 'down the pressure gradient', but because the Corioiis force acts at right angles to the direction of motion (to the right, if this is in the Northern Hemisphere), the equilibrium situation is one in which the direction of flow (dashed blue line) is at right angles to the pressure gradient.

As discussed in Section 3.3.1, the hydrostatic pressure at any given depth in the ocean is determined by the weight of overlying seawater. In barotropic conditions, the variation of pressure over a horizontal surface at depth is determined only by the slope of the sea-surface, which is why isobaric surfaces are parallel to the sea-surface. However, any variations in the density of seawater will also affect the weight of overlying seawater, and hence the pressure, acting on a horizontal surface at depth. Therefore, in situations where there are lateral variations in density, isobaric surfaces follow the sea-surface less and less with increasing depth. They intersect isopycnic surfaces and the two slope in opposite directions (see Figure 3.1 Kb)). Because isobaric and isopycnic surfaces are inclined with respect to one another, such conditions are known as baroclinic.

Geostrophic currents - currents in which the horizontal pressure gradient force is balanced by the Corioiis force - may occur whether conditions in the ocean are barotropic (homogeneous), or baroclinic (with lateral variations in density). At the end of the previous Section we noted that in the hypothetical ocean where the pressure gradient force was the only horizontal force acting, motion would occur in the direction of the pressure gradient. In the real ocean, as soon as water begins to move in the direction of a horizontal pressure gradient, it becomes subject to the Corioiis force. Imagine, for example, a region in a Northern Hemisphere ocean, in which the sea-surface slopes up towards the east, so that there is a horizontal pressure gradient force acting from east to west (Figure 3.12(a)). Water moving westwards under the influence of the horizontal pressure gradient force immediately begins to be deflected towards the north by the Corioiis force; eventually an equilibrium situation may be attained in which the water flows northwards, the Corioiis force acting on it is towards the east, and is balancing the horizontal pressure gradient force towards the west (Figure 3.12(b)). Thus, in a geostrophic current, instead of moving down the horizontal pressure gradient, water moves at right angles to it.

Moving fluids tend towards situations of equilibrium, and so flow in the ocean is often geostrophic or nearly so. As discussed in Section 2.2.1, this is also true in the atmosphere, and geostrophic winds may be recognized on weather maps by the fact that the wind-direction arrows are parallel to relatively straight isobars. Even when the motion of the air is strongly curved, and centripetal forces are important (as in the centres of cyclones and anticyclones), wind-direction arrows do not cross the isobars at right angles - which would be directly down the pressure gradient - but obliquely (see Figure 2.5 and associated discussion).

So far, we have only been considering forces in a horizontal plane. Figure 3.13 is a partially completed diagram showing the forces acting on a parcel of water of mass m, in a region of the ocean where isobaric surfaces make an angle 9 (greatly exaggerated) with the horizontal. If equilibrium has been attained so that the current is steady and not accelerating, the forces acting in the horizontal direction must balance one another, as must those acting in a vertical direction. The vertical arrow labelled mg represents the weight of the parcel of water, and the two horizontal arrows represent the horizontal pressure gradient force and the Corioiis force. Figure 3.13 Cross-section showing the forces acting on a parcel of water, of mass mand weight mg, in a region of the ocean where the isobars make an angle 9 (greatly exaggerated) with the horizontal. (Note that if the parcel of water is not to move vertically downwards under the influence of gravity, there must be an equal force acting upwards; this is supplied by pressure.)

Figure 3.13 Cross-section showing the forces acting on a parcel of water, of mass mand weight mg, in a region of the ocean where the isobars make an angle 9 (greatly exaggerated) with the horizontal. (Note that if the parcel of water is not to move vertically downwards under the influence of gravity, there must be an equal force acting upwards; this is supplied by pressure.) 