Internal tides, nonlinear internal wave trains, and mixing in the Faroe-Shetland Channel

Abstract

A semi-diurnal internal tide and trains of near-bed nonlinear internal waves are observed on the West Shetland slope, the shelf slope that forms the southeastern bank of the Faroe-Shetland Channel. The depth-integrated M₂ internal tide energy flux is 140 W m⁻1 up-slope and 154 W m⁻1 along-slope to the southwest. The majority of the energy flux is contained within the main pycnocline, where the slope is supercritical. A numerical model of the M₂ internal tide produces comparable across-channel energy fluxes, with a similar vertical structure, but larger along-channel energy fluxes by over a factor of two. The model output suggests the observed internal tide is generated at multiple sites, but dominated by an internal tide beam likely generated on the Faroe slope, across the channel. On the northern flank of the Wyville Thomson Ridge, at the southwestern end of the channel, modeled energy fluxes are over an order of magnitude larger, up to 10 kW m⁻1. The turbulent kinetic energy dissipation rate inferred from the observed internal tide energy flux, by assuming that all the energy in the pycnocline is dissipated on the slope, is 1:3 x 10⁻⁷ W kg⁻1, a factor of 4 larger than that inferred from Thorpe scale analysis (3x10⁻⁸ W kg⁻1). This suggests the level of mixing on the slope can be accounted for by the internal tide even if the majority of the energy is reected. The nonlinear internal wave energy flux is up-slope and intermittent; peak energy fluxes reach 200 W m⁻1, but are typically of order 10 W m⁻1. The wave trains are likely tidally forced and may be nonlinear manifestation of the internal tid