The asymptotic lake equations for an evanescent or emergent island

Jeudi 25 mars 14:00-15:00 - Lars Eric Hientzsch - Institut Fourier, Université Grenoble Alpes

Résumé : The lake equations arise as a geophysical two-dimensional model for the evolution of a fluid in a lake characterised by the geometry of its surface and its depth. Motivated by physical phenomena such as flooding, sedimentation and seismic activity, we investigate the stability of these equations under changes of both the geometry and the topography. More precisely, we first consider the singular limit for an evanescent island, namely an island shrinking to a point where the depth function vanishes. Second, we discuss the scenario of an emergent island. We obtain an asymptotic equation for both cases. In the former, a point vortex located at the point to which the island has collapsed is created. While the lake equations reduce to the two-dimensional incompressible Euler equations for a flat topography (constant depth), the lake equations are degenerate if the depth function vanishes at the boundary (beaches) or in the interior of the domain. We provide new uniform estimates in weighted spaces for the related stream functions that enable us to prove the compactness result.
This is joint work with Christophe Lacave and Evelyne Miot.

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