Wave and turbulence separation using dynamic mode decomposition

TL;DR

This paper introduces a new dynamic mode decomposition-based method for effectively separating wave and turbulence signals in oceanographic data, outperforming existing techniques and requiring minimal tuning.

Contribution

The paper presents a novel, signal-agnostic DMD-based wave-turbulence separation technique that needs minimal user input and demonstrates superior performance over existing methods.

Findings

The method accurately separates wave and turbulence components in various data sets.

Performance is optimal when wave energy exceeds turbulence energy.

The technique enables detailed turbulence analysis with minimal wave contamination.

Abstract

Separating the effects of waves and turbulence in oceanographic time series is an ongoing challenge because surface wave motion and turbulence fluctuations can occur at overlapping frequencies. Therefore, simple bandpass filters cannot effectively separate their dynamics. While more advanced decomposition techniques have been developed, they often entail restrictive assumptions about the wave and turbulence interactions, require synchronized measurements, and/or only decompose the signal spectrally without a time-series reconstruction. We present our new wave-turbulence decomposition technique which uses dynamic mode decomposition (DMD). The technique is signal-agnostic so it can be applied to any time series, and our only assumptions are that the waves and turbulence can be separated and that the waves are the most coherent features in the signal. Our approach requires minimal tuning, where the main user input is the wave frequency range of interest. To demonstrate the method, we apply it to synthetic, field, and laboratory data, and compare the results to other mode-based decomposition methods. A sensitivity analysis on the synthetic data shows that the most sensitive parameter to the accuracy is the rank truncation in the DMD, and that the decomposition performs the best when the wave energy in the signal is of equal or greater magnitude than that of the turbulence. Given the accuracy of our decomposition, we are able to analyze the velocity autocorrelation of the separated turbulence time series with minimal wave contamination. Overall, our decomposition method outperforms the other decomposition methods and provides for robust separation of the waves and turbulence, demonstrating wide applicability to ocean signal processing.