The pattern of surface waves in a shallow free surface flow

Abstract

This work presents new water surface elevation data including evidence of the spatial correlation of water surface waves generated in shallow water flows over a gravel bed without appreciable bed forms. Careful laboratory experiments have shown that these water surface waves are not well-known gravity or capillary waves but are caused by a different physical phenomenon. In the flow conditions studied, the shear present in shallow flows generates flow structures, which rise and impact on the water-air interface. It is shown that the spatial correlation function observed for these water surface waves can be approximated by the following analytical expression W(rho) = e(-rho 2/2 sigma w2)COS(2 pi L-0(-1)rho). The proposed approximation depends on the spatial correlation radius, sigma(w), characteristic spatial period, L-0, and spatial lag, . This approximation holds for all the hydraulic conditions examined in this study. It is shown that L-0 relates to the depth-averaged flow velocity and carries information on the shape of the vertical velocity profile and bed roughness. It is also shown that sigma(w) is related to the hydraulic roughness and the flow Reynolds number.