Wave and Turbulence Separation Using Dynamic Mode Decomposition

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 modal 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. Significance Statement When measuring physical, chemical, and biological quantities in the ocean, the measurements are often influenced by both waves and turbulence. Isolating the individual effects of waves and turbulence on those variables is important to a wide range of analyses, such as estimating how momentum, heat, and nutrients are mixed throughout the water column. In this work, we propose a new method to separate the wave and turbulence components in ocean-data time series. When tested on laboratory, field, and synthetic data, our method was able to separate the wave and turbulence components of a signal more effectively than previously proposed algorithms.