Wavelet-based predictions of bursting events in 2D Kolmogorov flow

Prediction of intermittent high-energy events (bursting events) is complicated by the fact that the characterization of such events using conventional Fourier-based methods involves many different frequencies. In this study, we therefore explore the use of wavelet-based techniques to predict such intermittent events. Two wavelet-based methods are compared: (1) a purely data-driven method using a wavelet-based Proper Orthogonal Decomposition (WPOD) and (2) a method that, along with data, uses the Navier-Stokes equations in the form of a wavelet-based resolvent analysis. The flow considered is 2D Kolmogorov flow, i.e. the Navier-Stokes equations forced by a sinusoidal body forcing over a 2-torus, which exhibits intermittent bursts of energy that are localised in time. Firstly, we find that the WPOD method is able to predict an oncoming bursting event. Secondly, the use of a wavelet-based resolvent analysis can give an improvement in prediction times albeit with an increase in the number of false-positives.