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Singularities of inertial waves

Time: Wed 2022-10-12 15.15 - 16.15

Location: Faxén, Teknikringen 8

Participating: Stéphane Le Dizès (IRPHE, CNRS - Aix-Marseille Université)

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Abstract: Stratified and/or rotating fluids support waves that can transport and dissipate energy away from their sources. These waves are suspected to play an important role in atmospherical sciences, oceanography, and in the dynamics of stars and planets. In the atmosphere, they transport momentum from the convective regions to the high altitude regions where they break and create mean flows. In the ocean, they are mostly generated by tides and winds and are expected to provide the missing contribution to the global energy budget of the ocean. In planets and stars, they are excited by gravitational effects or convection and could play a role in the generation of zonal flows and in dissipative processes.
In a fluid, rotating with the rotation rate Ω around the axis Oz and stably stratified with a constant buoyancy frequency N along the same axis, an harmonic forcing excites waves when its frequency ω lies within the inertia-gravity interval min(N,2Ω)< ω < max(N,2Ω). These waves propagate along cones (in 3D) or planes (in 2D) with a fixed angle with respect to the horizontal plane.
The cone (or the plane) tangent to the oscillating object or to a local topographical feature corresponds to a “critical” surface across which the wave field changes of nature. The singularity of the wave field across these surfaces if smoothed by viscosity gives rise to thin internal shear layers which possess some generic features.
In a closed domain, the waves reflect on boundaries while keeping the same propagation angle. Depending on the geometry and the propagation angle, they may contract and focus on a specific region of space forming an attractor. In the presence of weak viscosity, these attractors also manifest as thin internal shear layers.
For a rotating fluid in a spherical shell geometry, both critical surfaces and attractors can be present at the same time. Various wave patterns can then be obtained when the frequency and the nature of the harmonic forcing are changed. We show how these patterns can be obtained by monitoring the singularities of the inviscid
wave field.

Prof. Le Dizès' web page: