On a Technique for Measurement of Turbulent Shear Stress in the Presence of Surface Waves

Abstract

Surface waves can produce large biases in estimates of turbulent shear stress obtained from single-sensor measurements of velocity if there is even a small uncertainty in the orientation of either the velocity sensor or the principal axes of the wave-induced velocity field. The wave-induced bias can be diminished substantially by differencing measurements obtained from two velocity sensors separated by a distance larger than the correlation scale of the turbulence but small in comparison to the inverse wavenumber of the surface waves. If the scale separation is sufficiently large, then minus the density times half of the covariance between horizontal and vertical velocity differences is a nearly wave-free estimate of the average of the turbulent shear stresses at the two sensors. A theoretical analysis determines the bias associated with this technique under simplified conditions, in which waves and turbulence are uncorrelated and the waves are weakly nonlinear and narrow-banded in both frequency and direction. Order-of-magnitude estimates indicate that the technique can be used to obtain nearly unbiased estimates of near-bottom turbulent shear stress on continental shelves. A brief set of oceanic measurements demonstrates the success of the technique in practice.