Resonant flow of a stratified fluid influenced by damping over topography

Abstract

The influence of dissipation on the flow due to viscosity acting in the fluid as a whole over isolated topography is considered in the long wavelength, weakly nonlinear limit. The flow has been successfully modeled in the framework of the forced Korteweg–de Vries-Burgers’ equation. This model includes the effect of the viscosity of the fluid beyond the Korteweg-de Vries approximation. We develop a modulation theory for the undular bores produced upstream and downstream of the forcing, and validate it through numerical solutions, which show excellent agreement. Our findings demonstrate that the influence of viscosity is crucial in determining the properties of waves, such as the amplitudes of solitary waves and bore widths both upstream and downstream. Furthermore, we compare our numerical and theoretical results with published laboratory experiments, and find good agreement. These predictions also explain the discrepancies observed in previous experimental measurements, which can be attributed to the effects of viscosity.