About one of the mathematical models of viscous flow incompressible fluid above sandy bottom

Abstract

In this research we propose a mathematical model for the flows of a viscous incompressible fluid along an inclined plane under the action of gravity over a sandy bottom. The analysis was carried out in the linear instability of the flow and reduced the problem to finding the eigenvalues. Investigated and analyzed the questions of wave formation on the free and bottom surfaces of the liquid. The regions of flow instability are determined for any Froude numbers. Obtained results were compared with experimental data and with the results of other authors on this topic.