Inertia Currents

We should now briefly consider what happens when the wind that has been driving a current suddenly ceases to blow. Because of its momentum, the water will not come to rest immediately, and as long as it is in motion, both friction and the Coriolis force will continue to act on it. In the open ocean away from any boundaries, frictional forces may be very small so that the energy imparted to the water by the wind takes some time to be dissipated; meanwhile, the Coriolis force continues to turn the water cum sole. The resulting curved motion, under the influence of the Coriolis force, is known as an inertia current (Figure 3.7(a)). If the Coriolis force is the only force acting in a horizontal direction, and the motion involves only a small change in latitude, the path of the inertia current will be circular (Figure 3.7(b)).

Figure 3.7 (a) Various possible paths for inertia currents.

(b) Plan view showing inertial motion in the Northern Hemisphere. For details, see text.

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Figure 3.8 Plan view showing inertial motion observed in the Baltic Sea at about 57° N. The diagram shows the path of a parcel of water; if this path was representative of the general flow, the surface water in the region was both rotating and moving north-north-west. The observations were made between 17 and 24 August, 1933, and the tick marks on the path indicate intervals of 12 hours.

Figure 3.8 Plan view showing inertial motion observed in the Baltic Sea at about 57° N. The diagram shows the path of a parcel of water; if this path was representative of the general flow, the surface water in the region was both rotating and moving north-north-west. The observations were made between 17 and 24 August, 1933, and the tick marks on the path indicate intervals of 12 hours.

Figure 3.7 (a) Various possible paths for inertia currents.

(b) Plan view showing inertial motion in the Northern Hemisphere. For details, see text.

In an inertia current, the Coriolis force is acting as a centripetal force, towards the centre of the circle (Figure 3.7(b)). Now, if a body of mass m moves around a circle of radius r at a speed h, the centripetal force is given by centripetal force = 'JIl!— (3.5)

In this case, the centripetal force is the Coriolis force (given by mfu, where/ is the Coriolis parameter), so we can write:

centripetal force = Coriolis force, mu~

Dividing throughout by mu. this equation simplifies to:

If the motion is small-scale and does not involve any appreciable changes in latitude,/is constant and so the water will follow a circular path of radius /\ at a constant speed it. The time. T. taken for a water parcel to complete one circuit, i.e. the period of the inertia current, is given by the circumference of the circle divided by the speed:

This equation shows that in the 'ideal' situation, the only variable affecting T is/, i.e. latitude. Substituting appropriate values for sin <j) would show that at latitude 45°. T is approximately 17 hours, while at the Equator it becomes infinite.

Inertia currents have been identified from current measurements in many parts of the ocean. A classic example, observed in the Baltic Sea, is illustrated in Figure 3.8. Here a wind-driven current flowing to the north-north-west was superimposed on the inertial motion, which had a period of about 14 hours (the theoretical value of T for this latitude is a 14 hours 8 minutes) and died out after some nine or ten rotations.

In Question 3.4(a) we used the fact that Q, the angular speed of rotation of the Earth about its axis, is 7.29 x 10~5 s"1. This may also be written as 7.29 x 10"5 radians* s~', and is calculated by dividing the angle the Earth turns through each day (271) by the time it takes to do so (one day). Strictly, we should use one sidereal day, i.e. the time it takes the Earth to complete one revolution relative to the fixed stars. This is 23 hr 56 min or 86 160 seconds.

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