Dissipation of internal wave energy in the bottom boundary layer on the continental shelf

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Abstract
A theoretical model is developed considering a linear mode 1 internal wave train propagating into a shallow wedge, subject only to energy dissipation in the turbulent bottom boundary layer. The model incorporates variable vertical and cross‐shelf distributions of density. Internal wave energy dissipation is calculated by extending recently developed wave‐current interaction boundary layer theories, allowing for the nonlinear interaction of a surface wave, an internal wave, and a steady current in a rough turbulent boundary layer. Enhanced dissipation estimates using the wave‐wave‐current interaction drag formulation are contrasted to dissipation estimates using common linear and quadratic drag formulaitons. Order of magnitude differences are apparent between the linear and quadratic formulaitons. The boundary layer model formulation adjusts to the particular flow environment, sometimes behaving more like the linear formulation and other times more like the quadratic formulation. Dissipation of internal wave energy in the bottom boundary layer on the continental shelf is found to be of potential first‐order importance to the internal wave energy balance on the shelf, depending in a predictable way on shelf slope, density distribution, total flow environment, and bottom roughness.