The effects of the spatial distribution of bottom topography and bottom drag on seiche-induced wave train formation

Abstract

We consider the nonlinear, non-hydrostatic dynamics of seiches in small to medium-sized lakes. Using numerical simulations of shallow water equations modified to include weakly non-hydrostatic effects, we illustrate how spatially varying bottom drag and finite amplitude topography lead to the bending of wave trains that develop from the initial standing wave. For the case of variable topography, we discuss how the seiche and the wave trains that develop can resuspend material (e.g. nutrients) from the bottom of the lake and redistribute it in space. The numerical methods employed are spectrally accurate in space and second-order in time, yielding excellent accuracy and little numerical dissipation. We find that while the resuspension itself is largely due to the long standing waves at early times, the redistribution of nutrient distribution that is seen at later times is profoundly influenced by the development of the wave trains; a fundamentally non-hydrostatic effect.