Inertia-gravity wave dissipation and form drag. I. Finite depth effects
Phys. Rev. Fluids 11, 054804 – Published 27 May, 2026Erratum Phys. Rev. Fluids 11, 079901 (2026)
DOI: https://doi.org/10.1103/gnnb-vdkj
Abstract
Inertia-gravity waves present in a wide range of fluid dynamical contexts, necessitating a generalized and adaptable theory to accurately describe their behavior. We provide an analytical solution for form drag and velocity, in addition to the energy conversion rate of such waves excited by harmonic flow over a topographic source. Our analysis extends the investigations of Bell et al. [J. Fluid Mech. 67, 705 (1975)] and Llewellyn Smith et al. [J. Phys. Oceanogr. 32, 1554 (2002)] to consider a finite depth ocean without the hydrostatic or acoustic approximations. Eschewing these approximations enables consideration of waves in subinertial contexts (e.g., weak stratification, diurnal tides, or flow at high latitudes). The nonhydrostatic solution supports any waves forced at frequency between the stratification and Coriolis frequencies. The nonacoustic solution does not neglect the tidal excursion length and thereby enables superharmonics () to lie within the aforementioned interval, even when the fundamental frequency does not. The finite depth of the domain is found to suppress inertia-gravity wave power when the distance between reflections of the wave approaches the thickness of the wave beam. This suppression is enhanced in strongly nonacoustic contexts.