Coupled dynamics of interfacial waves and bed forms in fluid muds over erodible seabeds in oscillatory flows

Abstract

Recent field investigations of the damping of ocean surface waves over fluid muds have revealed waves on the interface between the thin layer of fluid mud and the overlying much thicker column of clear water, accompanied by bed forms on the erodible seabed beneath the fluid mud. The frequencies and wavelengths of the observed interfacial waves are qualitatively consistent with the linear dispersion relationship for long interfacial waves, but the forcing mechanism is not known. To understand the forcing, a linear model is proposed, based on the layer-averaged hydrostatic equations for the fluid mud, together with the Meyer-Peter-Mueller equation for the sediment transport within the underlying seabed, both subject to oscillatory forcing by the surface waves. If the underlying seabed is nonerodible and flat, the model indicates parametric instability to interfacial waves, but the threshold for instability is not met by the observations. If the underlying seabed is erodible, the model indicates that perturbations to the seabed elevation in the presence of the oscillatory forcing create interfacial waves, which in turn produce stresses within the fluid mud that force a net transport of sediment within the seabed toward the bed form crests, thus causing growth of both bed forms and interfacial waves. The frequencies, wavelengths, and growth rates are in qualitative agreement with the observations. A competition between mixing created by the interfacial waves and gravitational settling might control the thickness, density, and viscosity of the fluid muds during periods of strong forcing.