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arXiv · 2402.10749

Inertia-gravity waves in geophysical vortices

Jérémie Vidal·Yves Colin de Verdière
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Abstract

Pancake-like vortices are often generated by turbulence in geophysical flows. Here, we study the inertia-gravity oscillations that can exist within such geophysical vortices, due to the combined action of rotation and gravity. We consider a fluid enclosed within a triaxial ellipsoid, which is stratified in density with a constant Brunt-V\"ais\"al\"a frequency (using the Boussinesq approximation) and uniformly rotating along a (possibly) tilted axis with respect to gravity. The wave problem is then governed by a mixed hyperbolic-elliptic equation for the velocity. As in the rotating non-stratified case considered by Vantieghem (2014, Proc. R. Soc. A, 470, 20140093, doi:10.1098/rspa.2014.0093), we find that the spectrum is pure point in ellipsoids (i.e. only consists of eigenvalues) with smooth polynomial eigenvectors. Then, we characterise the spectrum using numerical computations (obtained with a bespoke Galerkin method) and asymptotic spectral theory. Finally, the results are discussed in light of natural applications (e.g. for Mediterranean eddies or Jupiter's vortices).

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Jérémie Vidal, Yves Colin de Verdière. 2024-02-16. Inertia-gravity waves in geophysical vortices. https://arxiv.org/abs/2402.10749

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