Six sets of particle image velocimetry (PIV) data from the bottom boundary layer of the coastal ocean are examined. The data represent periods of high, moderate and weak mean flow relative to the amplitude of wave-induced motion, which correspond to high, moderate and low Reynolds numbers based on the Taylor microscale (Re). The two-dimensional PIV velocity distributions enable spatial filtering to calculate some of the subgrid-scale (SGS) stresses, from which we can estimate the SGS dissipation, and evaluate the performance of typically used SGS stress models. The previously reported mismatch between the SGS and viscous dissipation at moderate and low Reynolds numbers appears to be related to the sparsity of large vortical structures that dominate energy fluxes.
Conditional sampling of SGS stresses and dissipation based on wave phase using Hilbert transforms demonstrate persistent and repeatable direct effects of large-scale but weak straining by the waves on the SGS energy flux at small scales. The SGS energy flux is phase-dependent, peaking when the streamwise-wave-induced velocity is accelerating, and lower when this velocity is decelerating. Combined with strain rate generated by the mean flow, the streamwise wave strain causes negative energy flux (backscatter), whereas the vertical wave strain causes a positive flux. The phase-dependent variations and differences between horizontal and vertical contributions to the cascading process extend to strains that are substantially higher than the wave-induced motion. These trends may explain the measured difference between spatial energy spectra of streamwise velocity fluctuations and spectra of the wall-normal component, i.e. the formation of spectral bumps in the spectra of the streamwise component at the wavenumbers for the transition between inertial and dissipation scales.
All the model coefficients of typical SGS stress models measured here are phase dependent and show similar trends. Thus, the variations of measured SGS dissipation with phase are larger than those predicted by the model variables. In addition, the measured coefficients of the static Smagorinsky SGS stress model decrease with decreasing turbulence levels, and increase with filter size. The dynamic model provides higher correlation coefficients than the Smagorinsky model, but the substantial fluctuations in their values indicate that ensemble averaging is required. The ‘global’ dynamic model coefficients indicate that the use of a scale-dependent dynamic model may be appropriate. The structure function model yields poor correlation coefficients and is found to be over-dissipative under all but the highest turbulence levels. The nonlinear model has higher correlations with measured stresses, as expected, but it also does not reproduce the trends with wave phase.