On Estimating Turbulent Reynolds Stress in Wavy Aquatic Environment

Several methods have been developed for the estimation of the turbulent Reynolds stress in wavy aquatic environment. They are based on different physical assumptions and often give discrepant results. It is practically difficult to quantify the uncertainties in these estimations. Using high-resolution velocity measurements of acoustic Doppler velocimeter (ADV) from a coastal benthic layer subject to moderate wave influence (the ratio of rms wave orbital velocity to current magnitude was 0.23-0.92), this study tests a Synchrosqueezed Wavelet Transform (SWT)-based method and three existing methods (i.e., the Coherence, Cospectra, and Ensemble Empirical Mode Decomposition [EEMD] methods) for wave-turbulence decomposition. In particular, we evaluate the performance of different methods for objective estimation of the turbulent Reynolds stress. Power spectra and cospectra analysis is conducted to quantify the uncertainties in the estimations. The results suggest that the Coherence method tends to overestimate the Reynolds stress due to incomplete removal of wave motions from the observed velocity records; the Cospectra method performs poorly because the empirical model does not fit the observed cospectra well; both the EEMD and SWT methods underestimate the Reynolds stress, as they tend to attribute turbulent fluctuations at frequencies in the vicinity of the wave frequencies to wave motions. In general, the SWT method performs best inducing lowest uncertainty in the Reynolds stress estimation. For the data set analyzed in this study, the estimations with the Coherence, Cospectra, EEMD, and SWT methods account for 70%, 50%, 51%, and 60% of the total covariance of horizontal and vertical velocities, respectively.