The location of thermal shelf fronts and the variability of the heights of tidal benthic boundary layers

Abstract

It is often hypothesized that the locus of a thermal shelf fronts is where the water depth (D) is equal to the thickness of the tidal frictional bottom boundary layer h. To determine the proper scales for tidal benthic boundary layers, we present simple, but rather general arguments which demonstrate that benthic boundary layers (BBL) in neutrally stratified environment must be defined by Ekman scale L_e = u_*/Ω, where u_* is friction velocity, based on the bottom stress τ_b = ρu²_*, ρ-water density, and Ω-Coriolis parameter. This result differs from those suggested by the numerical simulation of the formation of BBL in initially continuously stratified fluid, subject to a suddenly imposed barotropic pressure gradient as well as by direct observations of the intensity of turbulence close to the sea bottom, which indicated that the thickness of the well-mixed turbulent region close to the bottom of the sea is very often significantly less than L_e. Recently, Stigebrandt has argued that it can be explained by introducing the numerical constant λ in the expression h=λL_e (λ ͌ 0.2). We are trying here, as before to explain this by the influence of the imposed background stable stratification (with buoyancy frequency N), which limits the effective growth of BBL according to classical Ekman dynamics and creates a quasi-equilibrium thickness of BBL better characterized as h=bu_*/N where b is a numerical constant (b͌ 4–9 in agreement with Kitaigorodskii and Joffre). We also demonstrate that the latter result is not in disagreement with observations of the locus of shelf thermal fronts in the Irish Sea and the Gulf of Maine.