The sea bed boundary layer under random waves plus current

Abstract

The boundary layer under random waves alone, as well as under random waves plus current, has been examined using a dynamic turbulent boundary layer model; this is based upon the linearised boundary layer equations, with horizontally uniform forcing. The turbulence closure is provided by a high Reynolds number k− ε model. The model appears to be verified, as far as data exists, i.e., for sinusoidal waves alone as well as for sinusoidal waves plus a mean current. The time and space variation of the velocity, the turbulent kinetic energy and the shear stress within the bottom boundary layer have been examined. Correlations between boundary layer quantities due to the grouping of the largest waves in a realistic sea state have also been examined. A wave friction factor for random waves is proposed. Estimates of probability density functions for individual bottom shear stress maxima are given, for random waves alone as well as for random waves plus current. Superposition of a mean current on the waves at the outer boundary induces a drift and an enhancement of the flow quantities within the boundary layer. The enhancement of the friction velocity has been demonstrated and quantified. For the case of a non-zero angle between the waves and the current, the time variation of the horizontal direction of the friction velocity vector has been quantified. Estimates of the apparent roughness experienced by the current, in the presence of waves, are given. The resulting mean bottom shear stress for random waves plus current has been shown to agree reasonably well with that obtained by an equivalent sinusoidal wave plus current. The bottom friction under random waves alone has been shown to be in good agreement with that obtained by Madsen (1994), based on an equivalent sinusoidal wave.