## Question

ta) A body of water is carried .souihmmls from the Equator in a current, tit As the w ater mo\es south, how is does its planetary tonicity change'.' tiit How does this affect its relative vorticity'.'

thi What happens to the relative vorticity of a body of water if it is acted upon by;

tit winds blowing in a clockwise direction tin cyclonic winds in the Southern Hemisphere?

However, the situation is not quite as straightforward as this hecause the vorticity of a bod) of water is the sum of the vorticity of all the constituent particles of water. Consider, for convenience, a column of water moving 111 a current. For the purposes of this discussion, we can imagine the column of water spinning about its own axis, although its vorticity could of course be due to any type of rotatory motion (Figure 4.5). For simplicity, we can also assume thai the column is rotating anticlockw ise in the Northern Hemisphere, i.e. it has positive relative vorticity

What w ill happen if the rotating column of water becomes longer and thinner as a result of stretching, because it moves into a region of deeper sea-floor, for example? (Consider w hat happens w hen spinning ice-skaters bring their arms in close to their sides.)

Figure 4.8 (a) The angular momentum 0! a particle ol mass m moving with angular velocity <11 in a circle of radius r is given by mr2o>. (b) For the tot3l anguiar momentum (vorticity) of a stretched column of water to remain constant, the angular velocity cu of the panicles in the column must increase.

The simple answer is that, like the ice-skater, the column of water will spin faster, i.e. its relative vorticity will increase (become more positive). Looked at from (he point of view of angular momentum, I he angular momentum of each particle of water is »irin. w here r is the distance from the panicle (of mass m) to (he axis of rotation, and tu is the angular velocity (Figure 4.8(a)). When the column stretches, the average radius r decreases and so. for angular momentum to be conserved, w the speed of rotation must increase 1 Figure 4,S( hi). Because of the effect of changes in the length (£)) of lhe water column, (he property thai ¡s actually conserved is therefore 061/+ the absolute vorticity. but (/' + C)/l). the potential Vorticity.

The example given above is unrealistic because we have omitted consideration of variations 111./: (he planetary vorticity. In fact, in the real oceans, away from coastal boundaries and 01 her regions of large current shear, f is very much greater (han C, This means that (/+ iis effectively equal to /ZO and it is / that must change in response to changes in D: and as/is simply a function of latitude, it can only he changed by w ater changing iis latitude.

angular momentum = mr2to

cu small average e large to large average r small cu small average e large column stretches while conserving its angular momentum'vorticity