Spectral estimates of bed shear stress using suspended-sediment concentrations in a wave-current boundary layer

High-resolution time series of suspended-sediment profiles have been obtained using an acoustic backscatter system at an inner shelf site (North Carolina) where flows are dominated by wind-driven currents and waves. We analyzed the spatial and temporal structure of near-bed turbulence in particle-transporting flows and scalar-like fluctuations of suspended-sediment concentrations. An important element of our analysis is a new inertial dissipation method for passive tracers to estimate the shear stress acting on the seabed, using the spectral properties of suspended sediment concentrations observed by acoustic backscatter sensors. In flows that provide adequate separation of the scales of turbulence production and dissipation, a sufficiently thick constant stress wall layer, and significant sediment suspension, frequency (or associated wave number) spectra of near-bed sediment concentration exhibit a -5/3 slope in the inertial subrange that spans frequencies of order 1 Hz. This observation suggests that the suspended sediment is effectively a passive tracer of turbulent fluid motions. Inversion of the relevant, Kolmogorov scaling equations yields estimates of the shear velocity that agree reasonably well with other, independent and widely used measures. High- and low-frequency limits on application of the inertial dissipation method to sediment concentration are related to the inertial response time of sediment particles and the sediment settling timescale. We propose that, in future applications, the inertial dissipation method for passive tracers can be used to estimate either the shear velocity, effective settling velocity of suspended sediment (or equivalent particle size) or dynamic bed roughness if two of these three quantities are independently known.