Wave-turbulence decomposition and turbulence parameterization in aquatic wave environments using improved Synchrosqueezed Wavelet Transform (iSWT)

Abstract

Accurate quantification of near-surface turbulence is essential for understanding the dynamics of turbulent mixing and mass transport in aquatic systems. However, field measurements of near-surface flow velocities often include contributions from surface gravity waves. For the quantification of turbulence and related transport processes, robust methods are needed to separate wave motion from the turbulent velocity fluctuations. In this study, we evaluated the performance of five different methods for wave-turbulence decomposition in estimating turbulent kinetic energy, Reynolds stress and turbulent kinetic energy dissipation rate. The methods include Ensemble Empirical Modal Decomposition (EEMD), Phase method (PH), Variational Mode Decomposition (VMD), Synchrosqueezed Wavelet Transform (SWT) and improved Synchrosqueezed Wavelet Transform (iSWT). We used these methods for a re-analysis of high-frequency velocity measurements from the water surface of the Kitinen River, Finland. The results show that the different methods remove the wave component to varying degrees, whereas the performance of the VMD method appeared insufficient. The estimated turbulent kinetic energy and Reynolds stresses were generally smaller than 30 % of those calculated from the unprocessed velocity measurements. In terms of energy spectra, the EEMD, PH, SWT and iSWT methods all provide a better removal of wave energy, but the EEMD and SWT methods resulted in substantial energy notches in the wave frequency band, resulting in a significant underestimation of the turbulent velocity fluctuations. In contrast, iSWT achieves the decomposition of wave and turbulence components by applying an optimal decomposition degree index $p_{\mathrm{opt}}$, which maximizes the retention of turbulent velocity fluctuations. Application of the inertial dissipation method for estimating dissipation rates of turbulent kinetic energy from the spectra of separated turbulent velocities. The results showed that the iSWT method resulted in the longest inertial subrange, and allowed for most but also has very good robustness spectral fits for dissipation rates ranging from 1.33 × 10⁻⁷ W/kg to 1.06 × 10⁻⁵ W/kg. Using dissipation rate estimates from an advanced methods explicitly considering wave-turbulence interactions as a reference, the iSWT method showed the closest agreement, whereas the dissipation rates estimated from velocities processed by the other four methods were generally lower. The newly proposed method is able to provide accurate estimates of dissipation rates by robustly separating the turbulence from wave-affected velocities compared to the four tested existing methods.