Coupled estimation of incoherent inertia gravity wave field and turbulent balanced motions via modal decomposition

Abstract. The non-linear interactions between an internal wave field propagating through a balanced turbulent flow make the incoherent propagation of ocean internal tides difficult to understand and to predict. In this paper, we propose a data-driven method that extracts the structures of a wave field correlated with the fluctuations of the background flow, exploiting the fact that the scattering of the wave results from a quadratic nonlinearity involving both types of motions. The method consists of applying the extended proper orthogonal decomposition method to the complex wave envelope, extracted by complex demodulation, in order to provide the spatial structures of an incoherent wave contribution correlated to the proper orthogonal decomposition modes of the balanced motion. Using the rotating shallow water as a canonical model for wave / balanced flow interactions, we describe the connection between the variability of the jet and the incoherence of the internal wave, which provides some theoretical foundations to the proposed method. This expected connection is then confirmed by numerical simulations of the rotating shallow water model, and the variability modes of the jet and wave field are analysed. Finally, an algorithm for estimating the jet component and the associated wave field from single snapshots of the sea level height is proposed and tested using outputs from numerical simulations. We show that such algorithm provides a valuable coupled estimate of the two dynamics, especially in configurations where the wave signal is small compared to the jet.