Sea ripple formation: the turbulent boundary layer case

This study presents a predictive theory of ripple formation beneath sea waves. The theory is based on a linear stability analysis of a flat sandy bottom subject to an oscillatory flow. The flow regime in the bottom boundary layer is assumed to be turbulent; hence previous works on the subject, which considered a laminar flow, are extended in a more relevant range of the Reynolds number. The turbulent stresses are described by means of the constant eddy viscosity model proposed by Sleath in 1991 and a two time-scale approach is used to decouple fluid motion from bottom time development. A closed form solution is found for the turbulent oscillatory how over a fixed wavy wall and the time development of the bottom perturbation is determined by means of sediment continuity equation. The conditions for ripple appearance are determined along with their wavelength as they form. A comparison between theoretical findings and experimental data supports the validity of the present approach.