A novel approach for wave-turbulence decomposition

Decomposing turbulence from waves remains challenging due to frequency overlap and wave-turbulence interactions. Existing decomposition methods, e.g., moving average, energy spectrum analysis, and synchrosqueezed wavelet transform (SWT), produce inconsistent turbulence estimates. Here, we introduce a rotating-coordinate-based method (RoCoM), founded on two assumptions: (1) the energy spectrum in the cross-wave direction remains unaffected by wave orbital velocities, and (2) wave-wise and vertical turbulence spectra are linearly proportional to the cross-wave spectrum, with proportional constants derived from frequencies higher than the wave-dominated frequency range. Both assumptions were validated with observational data collected from the Changjiang Estuary. Comparative analyses using both in-situ observations and controlled laboratory experiments show RoCoM avoids the energy trough problem inherent in the moving average and SWT methods, yielding the most accurate power spectra and turbulent kinetic energy (TKE) estimates. In-situ data reveal that the relative errors of RoCoM are approximately 16 % for total TKE and about 6 % for TKE within the wave-dominated frequency range. Laboratory experiments further confirm its superior accuracy, demonstrating relative errors of approximately 14 % for total TKE and about 7 % for wave-band TKE. RoCoM holds significant implications for marine material transport and coastal energy development by providing robust and precise turbulence and wave energy estimates. Nonetheless, its application is currently best suited for scenarios with predominant wave propagation from a single direction, while SWT remains advantageous in environments characterized by broader directional wave spreading.