Fluid circulation and seepage in lake sediment due to propagating and trapped internal waves

Abstract

It has long been known that surface gravity waves induce significant seepage through the porous layer found at the lake bottom. Away from coastal regions, however, the pressure signature of surface waves at the lake bottom is weak. We consider fully nonlinear internal gravity waves, whose long wavelength and slow motion implies a sustained and strong pressure perturbation even in the deep regions of the lake. We argue that internal waves can induce significant seepage through the sediment layer, in regions where surface gravity waves have negligible impact. The pressure profile at the fluid–porous layer interface is computed from the “exact” Dubreil‐Jacotin‐Long theory, giving a reliable profile even for large waves. This profile is used in conjunction with Darcy's law to compute the seepage within the porous region. We find that the geometric distribution of seepage is strongly controlled by both the ratio of porous media thickness to the horizontal length of the pressure perturbation, and the bottom topography, when it is present. Based on work on the interaction of internal solitary waves with the bottom boundary layer, we develop a model to account for the changes in permeability due to wave‐induced instabilities in the bottom boundary layer and enhanced benthic turbulence. This turbulence acts to unplug the pores near the surface by lifting the detritus that clogs them. The resulting changes in permeability significantly enhance exchange between the free fluid and the porous medium on the downstream side of the wave.