Speaker
Description
We study the shallow water model, which is a simplified model obtained from the Navier-Stokes equations by imposing the existence of a free surface and assuming the vertical height of the fluid to be small compared to the horizontal dimensions. This model allows to describe turbulent cascades in oceans near the coast or in highly stratified fluids. Moreover, the shallow water equations can be fruitfully used to benchmark ideas and techniques to be later applied to the full 3-dimensional problem of surface gravity waves. Different regimes and scaling laws are observed in experiments and direct numerical simulations, suggesting a rich phase diagram depending on the parameters of the model. Existing theoretical analyses are mainly based on the statistical closure known as Wave Turbulence, which is inherently perturbative and cannot access all the different regimes. In this work, we use the Functional Renormalization Group to explore the phase diagram of the shallow water model beyond the perturbative limit. We compute in particular the energy spectrum to characterize the different cascades and scaling regimes depending on the model parameters.
| Affiliation | Côte-d'Azur University, INPHYNI (Nice), LPMMC (Grenoble) |
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| Career status | PhD student |