Energetics of nonlinear internal waves generated by tidal flow over topography

Abstract

An in-house fully nonlinear, nonhydrostatic numerical model is utilized for simulations of internal solitary waves (ISWs) generated by tidal flows over a Gaussian sill topography. A complete, rigorous theoretical framework is then adopted for the energetics analysis of these ISWs. The ratio of topographic amplitude to the total water depth is fixed, and the tidal excursion parameter (ε) and slope parameter (γ) are varied by changing the imposed barotropic velocity and the horizontal scale of the topography. It is found that the energy input, conversion, and radiation rates all increase monotonically with ε. They peak when the bottom topography is critical (γ=1). The energy input is generated by the pressure difference across the domain. The energy conversion rate in percentage (normalized by the corresponding input rate) decreases almost linearly as ε increases. The larger the slope parameter, the higher the conversion percentage. The baroclinic radiation rate in percentage (normalized by the corresponding conversion rate) increases first and then decreases as ε increases. It gets maximum near ε=0.15, which corresponds to the emergence of ISWs in the flow field. The larger the slope parameter, the smaller the radiation percentage. At small ε value when the flow field is in the linear internal tide regime, the conversion and radiation percentages all agree very well with the results in existing literature (Kang and Fringer, 2012) for the Davidson Seamount. The barotropic and baroclinic dissipation percentages behave very differently. While the barotropic one is larger for smaller γ, the baroclinic one is larger for larger γ. The present work presents a relatively complete energy budget analysis of ISWs generated by tidal flow over a Gaussian sill topography.