Mathematical modeling of penetration of a mixed layer into a stratified fluid

A problem is proposed that reflects the flow in a circular trough more precisely. At the end cross sections, the free-flow condition is imposed at the outlet boundary and also the condition that the flow at the inlet boundary is an uninterrupted continuation of the flow at the exit from the considered domain solution of the problem. The processes of vertical turbulent mixing are described on the basis of the complete (e - ε) model, while the coefficients of horizontal turbulent exchange are determined by the Richardson formula. This formulation of the problem takes into account the friction stress of the side walls.