Gravity Waves on Turbulent Shear Flow: Reynolds Averaged Approach

Abstract

Gravity waves propagating over free-surface flows with shallow depth are well-known phenomena. The small-amplitude sinusoidal wave and Korteweg-de Vries (KdV) equations are based on potential-flow theory being widely used to describe water-wave propagation. The KdV equation leads to two basic flow patterns, as follows: (1) cnoidal waves, and (2) solitary waves. However, in case of a real Newtonian fluid, the bed resistance and the rapid motion of fluid generate turbulence (eddies) in the medium. The effects of turbulence are taken into account in this paper by using the equations for the surface elevation