22 May 2024
 | 22 May 2024
Status: this preprint is open for discussion.

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

Igor Maingonnat, Gilles Tissot, and Noé Lahaye

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.

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Igor Maingonnat, Gilles Tissot, and Noé Lahaye

Status: open (until 17 Jul 2024)

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Igor Maingonnat, Gilles Tissot, and Noé Lahaye

Model code and software

Codes to compute the methods in this article. Igor Maingonnat

Interactive computing environment

Notebooks for diagnostics, visualisation and estimates. Igor Maingonnat

Igor Maingonnat, Gilles Tissot, and Noé Lahaye


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Short summary
The entanglement of waves and currents in observational data complicates their respective estimation. We propose a data-based method providing a reduced set of modes associated with waves and currents respectively. Correlations between the two bases coordinates can be deduced, allowing us to perform a coupled estimation of these two physical processes. This methodology is able to produce estimates from an instantaneous observation of sea surface height, and for a strong jet signal.