Energetics of mode-1 internal waves interacting with topographic ridges of varying height and slope

Abstract

Energetics of mode-1 internal waves interacting with topographic ridges are investigated using high-resolution two-dimensional simulations at spatial scales of $O(100)$ m that span between classical laboratory-scale ( $O(10)$ m) and field-scale simulations ( $O(1000\unicode{x2013}10\,000)$ m). This paper focuses on the energetics of wave–topography interaction, with emphasis on systematically examining the partitioning of the incident wave energy as a function of wave forcing and topographic parameters. Partitioning of energy into the transmitted, reflected and dissipated components is quantified as a function of wave Froude number $Fr=U_0/c_{ph}$ ( $U_0=$ velocity amplitude of forcing and $c_{ph}=$ internal wave celerity), slope criticality $=\gamma /s$ , where $\gamma =$ topographic slope and $s=$ wave characteristic slope, and the ratio of topographic height $h_t$ to water depth $d$ . As $Fr$ increases, dense fluid from the base of the stratified water column surges upslope with significant vertical inertia, leading to the formation of internal boluses that plunge over and onto the downstream side of the ridge, resulting in elevated dissipation. Results show that non-hydrostatic contributions to the total energy flux are significant (up to 50 %). Analysis of the energy flux budget shows that transmitted energy flux decreases monotonically as $\gamma /s$ increases for any given $Fr$ and $h_t/d$ . At critical slopes ( $\gamma /s=1$ ), the transmitted energy flux scales as a linear function of $h_t/d$ , with a mild dependence on $Fr$ , a key result that can be useful in energy flux parameterizations. Reflected energy flux exhibits a nonlinear dependence on the ridge height, increasing sharply when $h_t/d > 0.5$ . Dissipation is enhanced at critical slopes, with a plateau evident for $\gamma /s \ge 1$ and $h_t/d = 0.5$ for all $Fr$ .