Computation of flows in stratified liquids and gases with free upper boundary

Explicit method for computation of convective flows in stratified liquids and gases under the wind stress on a free upper surface is proposed. Numerical method is based on the modified hydrostatic approximation, which is formulated in this paper. It allows to use this method in wide range of regions both for the case of large horizontal scale (in comparison with the vertical one) and for regions with comparable horizontal and vertical scales. Numerical solutions are presented.