Steady Flow Regimes in the Problem of Intense Wind-Driven Circulation in a Thin Layer of Viscous Rotating Fluid

Abstract

The problem of wind-driven circulation in a thin layer of homogeneous viscous rotating fluid is considered. In the limit of small Froude and Burger numbers it is described by two parameters—the Rossby number proportional to the forcing and the Ekman number. For small Ekman numbers and moderate Rossby numbers, the regimes of steady fluid circulation are investigated through numerical simulations of a Kármántype flow. Two different types of steady flows are shown to exist, and their physical interpretation based on a simple analytical model is proposed. A regime diagram on the plane of problem parameters is provided. The simultaneous existence of steady flows of two different types turns out to be possible in some domain of parameters, i.e., there is a dependence of the stationary solution to the problem on initial data. The asymptotic dependence of steady flow characteristics is investigated in the limit of small Ekman numbers.