Variational Mode Decomposition for estimating critical reflected internal wave in stratified fluid

TL;DR

This paper introduces a modified Variational Mode Decomposition method to effectively isolate reflected internal waves during critical reflection in stratified fluids, enabling better comparison with theoretical models.

Contribution

The study adapts and applies a 2D-VMD-prox decomposition method specifically for internal wave critical reflection, improving wave separation performance.

Findings

Enhanced wave decomposition accuracy in critical reflection scenarios

Validated the decomposition method against viscous and nonlinear models

Improved understanding of shear rates during internal wave reflection

Abstract

The shear resulting from internal wave reflections can play a crucial role in the transport and resuspension of sediments in oceanic conditions. In particular, when these waves undergo a \textit{critical reflection} phenomenon, the reflected wave can produce a very large shear. Separating the reflected wave from the incident wave is a technical challenge since the two waves share the same temporal frequency. In our study, we present a series of experimental measurements of internal waves in \textit{critical reflection} configuration and we analyze them using the 2D-VMD-prox decomposition method. This decomposition method was adapted to specifically decompose waves in an internal wave critical reflection, showing an improvement in its performance with respect to preexisting internal wave decomposition methods. Being able to confidently isolate the reflected wave allowed us to compare our results to a viscous and non-linear model for critical reflection, that correctly describes the dependence of the shear rate produced in the boundary as a function of the experimental parameters.