Tidal mixing in sill regions: influence of sill depth and aspect ratio

Abstract

A non-hydrostatic model in cross-sectional form with an idealized sill is used to examine the influence of sill depth (hs) and aspect ratio upon internal motion. The model is forced with a barotropic tide and internal waves and mixing occurs at the sill. Calculations using a wide sill and quantifying the response using power spectra show that for a given tidal forcing namely Froude number Fr as the sill depth (hs) increases the lee wave response and vertical mixing decrease. This is because of a reduction in across sill velocity Us due to increased depth. Calculations show that the sill Froude number Fs based on sill depth and across sill velocity is one parameter that controls the response at the sill. At low Fs (namely Fs ≪ 1) in the wide sill case, there is little lee wave production, and the response is in terms of internal tides. At high Fs, calculations with a narrow sill show that for a given Fs value, the lee wave response and internal mixing increase with increasing aspect ratio. Calculations using a narrow sill with constant Us show that for small values of hs, a near surface mixed layer can occur on the downstream side of the sill. For large values of hs, a thick well-mixed bottom boundary layer occurs due to turbulence produced by the lee waves at the seabed. For intermediate values of hs, “internal mixing” dominates the solution and controls across thermocline mixing.