A simple model for vertical profiles of velocity and suspended sediment concentration in straight and curved submarine channels

Abstract

We develop a simple model to describe vertical profiles of velocity and suspended sediment concentration in submarine channels. We consider a conservative turbidity current flowing in a confined channel under steady and uniform flow conditions. The turbulence closure for density stratification is adapted from the model of Mellor and Yamada (1982). Solutions are obtained for both straight and constant curvature channels. In the latter case, in order to evaluate the secondary flow induced by curvature, we take advantage of the fact that the ratio of flow depth to radius of curvature is typically small in the field, which leads to a solution of the governing equations through an appropriate asymptotic expansion. Comparison of results on longitudinal velocity profiles in straight channels with experimental and field observations shows an excellent agreement and allows for the prediction of concentration profiles and suspended sediment size from known bed slope, current thickness, and normalized velocity at the turbidity current-ambient water interface. The model is able to capture the presence of multiple circulation cells on the vertical and the sense of rotation of the near-bottom secondary flow that can be either reversed (directed outward) or normal oriented (directed inward) with respect to the classical fluvial orientation. The parameters controlling the orientation of secondary flow in submarine channels are identified, and the implications on the bed morphology are discussed. The potential use and future developments of the present approach are also discussed.