Evolution of bed forms produced by clarified turbulent flow over a non-cohesive bed

This paper considers the problem of purified turbulent flow over an erodible bed. A mathematical model of the problem is proposed which includes the Reynolds equations and transport equations for turbulent kinetic energy and turbulence dissipation. The bed surface evolution is described using the bed deformation equation and the original analytical model of bed-load sediment transport. An algorithm based on the control volume method is proposed for solving the problem. Numerical solution of the problem shows that when the bed is eroded by a purified flow, a wave packet of low-steepness bed waves is formed. It is also shown that the velocity of bed waves obtained by the numerical solution is in good agreement with the velocity of bed waves calculated by asymptotic analytical formula.