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.

Abstract. This paper presents developments of the Harniltonian Approach to problems of fluid dynamics, and also considers some specific applications of the general method to hydrodynamical models. Nonlinear gauge transformations are found to result in a reduction to a minimum number of degrees of freedom, i.e. the number of pairs of canonically conjugated variables used in a given hydrodynamical system. It is shown that any conservative hydrodynamic model with additional fields which are in involution may be always reduced to the canonical Hamiltonian system with three degrees of freedom only. These gauge transformations are associated with the law of helicity conservation. Constraints imposed on the corresponding Clebsch representation are determined for some particular cases, such as, for example. when fluid motions develop in the absence of helicity. For a long time the process of the introduction of canonical variables into hydrodynamics has remained more of an intuitive foresight than a logical finding. The special attention is allocated to the problem of the elaboration of the corresponding regular procedure. The Harniltonian Approach is applied to geophysical models including incompressible (3D and 2D) fluid motion models in curvilinear and lagrangian coordinates. The problems of the canonical description of the Rossby waves on a rotating sphere and of the evolution of a system consisting of N singular vortices are investigated.

Abstract. Multi-petal, rotating vortices can form in twodimensional flows consisting of an inviscid incompressible fluid under certain conditions. Such vortices are principally nonlinear thermo-hydrodynamical structures. The proper rotation of these structures which leads to time-dependent variations of the associated temperature field can be enregistred by a stationary observer. The problem is analyzed in the framework of the contour dynamics method (CDM). An analytical solution of the reduced equation for a contour curvature is found. We give a classification of the solutions and compare the obtained results with observational data.

Abstract. Two-dimensional vortex pairs are frequently observed in geophysical conditions, for example, in a shelf zone of the ocean near river mouths. The main aims of the work are to estimate the space scales of such vortex structures, to analyze possible scenarios of vortex pair motion and to give the qualitative classification of their trajectories. We discuss some features of the motion of strong localized vorticity concentrations in a given flow in the presence of boundaries. The analyses are made in the framework of a 2D point vortex model with an open polygonal boundary. Estimations are made for the characteristic parameters of dipole vortex structures emitted from river mouths into the open ocean.

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