Two-dimensional vortex motions of fluid in harbor-like basins at large Reynolds numbers

This article considers the topology of the vortex regimes generated in harbor-like basins by the external potential long shore current at large Reynolds numbers. The proposed theory discusses the issues of what solution compatible with the Prandtl-Batchelor theorem for inviscid fluids, and under what conditions, may be realized as an asymptotic state of the open hydrodynamical system. The analysis developed is based on the variational principle. We formulated a validity criterion according to which stationary regimes of dissipative systems may be considered as extremals of a variational inviscid problem. In particular, such a situation is possible when the dissipative functionals represent some functions of motion invariants of the same problem. It is shown that the steady state corresponds to the circulational regime in which the system has minimal energy with the fixed enstrophy. This state is fixed by the Reynolds number. The approach that is formulated is applied to the model of a rectangular harbor-like basin in order to obtain the relation between the Reynolds number, the geometry factor and the topological number characterizing the number of vortex cells. (C) 1998 American Institute of Physics.