Comparative Analysis of Two Models of the Two-Layer Fluid Motion by means of Ekman's Approximation

Two Ekman's type models for stationary wind-driven motion of two-layer fluid are proposed. Upper and lower layers are homogeneous with different densities. The analytic solutions in the two-dimensional and three-dimensional cases are found for this models. For the 2-D case it is assumed that the bottom of the water basin is not flat and the vertical turbulent exchange coefficients in upper and lower layers depend on the depth. For the 3-D case the vertical turbulent exchange coefficients are constant in each layer and the bottom of the water basin is flat. The obtained solutions could be useful for the evaluation of the boundary location between layers and as a test in the analysis of computational algorithms which are applied for solving problem of the wind current in a two-layer liquid.