Axially symmetric steady solutions of equations describing ice drift under the influence of cyclonic and anticyclonic wind vortex are constructed and analysed in cases when the ice has elastic-plastic rheology and viscous-plastic rheology. In both cases the solution consists of the ring where the ice is in the plastic state, and the inner kernel and outer ring where the ice stresses are located inside the yield curve. Natural boundary conditions in the origin, at the plastic ring boundaries and on the periphery of the outer ring are formulated. Elastic-plastic solutions satisfying boundary conditions are constructed and analysed in case of cyclonic and anticyclonic wind vortexes. V viscous-plastic solutions have singularity in the origin in case of anticyclonic wind. In case of cyclonic wind the ice thickness grows exponentially at the periphery of the outer ring and the angular velocity of ice drift tends to constant value.
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