Spectral Estimates of Bed Shear Stress at Subcritical Reynolds Numbers in a Tidal Boundary Layer

Abstract

Velocity measurements from five levels in the constant-stress region of a neutrally stratified turbulent boundary layer are used to show that below a critical height the spectral energy density in the inertial subrange remains constant at a magnitude appropriate to the critical height. Huntley used this proposition to devise a modification to the inertial-dissipation method of estimating time-averaged bed shear stress, applicable when the velocity is measured below the critical elevation. By applying the modified method here, spectral estimates of bed stress from below the critical height were caused to collapse onto a single true value. Without the modification, the estimates of bed stress were a strong function of elevation at which the velocity was measured, which is incompatible with a constant-stress layer governed by a single velocity scale. The data are from a tidal boundary layer above an embedded wave boundary layer. The mean flow in this region experienced a hydraulic roughness that was partly attributable to nonlinear wave–current interaction in the wave boundary layer, but the realization of the turbulent-velocity spectra, from which bed shear stress was inferred, was not compromised by the wave-orbital velocities. The behavior of the spectra below the critical height is due to scale-separation effects on the energy cascade through the inertial subrange of the turbulent-velocity spectra.