Eddy viscosity and Eulerian drift over rippled beds in waves

Abstract

This paper reports the results of an experimental study of the Eulerian drift induced by weakly asymmetrical progressive waves in the bottom boundary layer over rippled beds in the transitional flow regime. Fourteen tests were carried out in a wave flume and one test in a steady flow flume for the estimation of the Nikuradse roughness length k s of the artificial rippled bed which was used. The fluid velocities were measured with a two-component laser-Doppler anemometer. The edge of the bottom wave boundary layer is estimated to be located at one Nikuradse roughness length above the level midway between crest and trough of the ripples. Momentum transfer in this boundary layer is dominated by organized vortices. An analytical model based on a time-varying eddy viscosity was developed by Davies and Villaret [J. Geophys. Res. 104 (C1) (1999) 1465] for the estimation of the wave-induced Eulerian drift above rippled and very rough beds in the turbulent flow regime. Present data show that the applicability of this model can be extended to the “lower” part of the transitional flow regime in the parameter ranges 1000≤ R≤6500 and 1≤ a/ k s≤3, where R is the flow Reynolds number and a is the orbital amplitude of fluid, if adjusted values of the model coefficients which represent the variation amplitude of the symmetrical and asymmetrical time-varying components of the eddy viscosity are used. The drift at the edge of the boundary layer is oriented in the direction of wave propagation in the transitional flow regime, while this drift is oriented in the opposite direction in the turbulent flow regime. The vertical profiles of Eulerian drift, horizontally averaged over a ripple length, are also compared with Longuet-Higgins' [Philos. Trans. R. Soc. Lond., A 245(903) (1953) 535] solution for a laminar flow above a smooth bed and with Nielsen's [Coastal bottom boundary layers and sediment transport. Advanced Series on Ocean Engineering, Vol. 4, World Scientific, Singapore, Chap. 1, pp. 40–60, 1992] solution involving a time-invariant eddy viscosity for turbulent flows over fairly rough beds.