Approximate two-dimensional equations for vortex flows in a plane layer with rigid boundaries

This paper is concerned with the approximate two-dimensional equations describing turbulent vortex flows in plane liquid layers. These equations were earlier obtained by the author using a shallow-water approximation and with no regard for circulation flows in the cross-section of the layer. It is shown that circulation flows initiated by the centrifugal effect caused by the vortex flow have only a weak effect on the liquid flow in a plane layer and, therefore, can be ignored.