Within the framework of the rigid body hypothesis, the influence of external torques acting on a rotating water lens in a stratified ocean is examined and a hypothesis about the angular motion of objects of such kind is constructed. The structure of the external torques acting on the lens is investigated and their magnitudes and influence on the overall picture of the motion of the lens about its centre of mass are estimated. It is shown that the hydrostatic buoyancy torque is the most important of such torques, it being orders of magnitude greater than the Coriolis torque and the torque due to virtual masses, and also the gravitational torque and other torques. The friction torque can promote stabilization of the angular motion and lead to the appearance of a steady regime. The results obtained are in agreement with the observed motion of oceanic formations.

The problem of the equilibrium shapes of rotating vortices in a stratified ocean, which is in a statically stable state, is considered within the framework of the model of an ideal incompressible fluid. An equilibrium shape is a surface on which the pressures in the vortex and in the ocean are equal, in which case, on this surface the normal components of the velocities of the media are equal to zero, but a discontinuity of the tangential components is allowed. The case of stratification of the media along the local vertical is considered. The external medium (the ocean) may consist of several layers, differing sharply in density.

A model formulation of the problem of the equilibrium shapes of a rotating oceanic lens of uniform density, the centre of which is at rest relative to the Earth is considered. All the components of the angular velocity of rotation of the Earth are taken into account, unlike, for example, in oceanography, where only one vertical component of this velocity is considered. The ocean surrounding the lens is assumed to be at rest, and its density is assumed to have a linear distribution. The equilibrium shape is the surface on which the pressures in the lens and in the ocean are equal, and here, on this surface, discontinuity of the tangential components of the velocities is permitted at points of both media. The exact solution of this problem, obtained earlier in [1] for the case of a uniform gravitational field of the Earth, is extended to the case of a potential gravitational field, approximating the actual field, taking into account of the variable nature of the centrifugal force field. The solution is approximate in nature and makes it possible, for example, to indicate the lower limit of the range of angular velocities of proper rotation of the lens, starting from which a more precise allowance for the gravitational field of the Earth is necessary, since it begins to have a considerable effect on the type of equilibrium shape sought. (C) 2004 Elsevier Ltd. All rights reserved.