Oscillatory drift of deep cold eddies

Abstract

This paper supplements an earlier one on the dynamics of cold isolated eddies situated on a sloping oceanic floor ( Nof, 1983a, Deep-Sea Research, 29, 171–182). The lens-like eddies under investigation correspond to cold patches bounded by an interface that intersects the slopping floor along a closed curve. A wide range of possible time-dependent migration patterns is explored analytically. Nonlinear solutions are constructed by separating the equations governing the migration from those governing the eddy's interior. It is shown that, in addition to the known steady migration at 90° to the right of the downhill direction discussed previously, oscillatory migration is also possible. This time-dependent migration corresponds to a nonlinear eddy that drifts along a cycloid. The asymmetrical oscillations are of the inertial period. They are superimposed on a main migration path which, as in the steady migration case, is directed along a straight line whose orientation is at 90° to the right of the downhill slope. To an observer riding with the eddy, the circulation within the eddy appears to be steady whereas the migration is time dependent. As in the steady translation case, the drift is entirely independent of the eddy's size, intensity, and depth. It depends only on the density difference between the eddy and the environment, the gravitational acceleration, the bottom slope, and the Coriolis parameter. Application of this theory to various eddies situated on the ocean floor is discussed.