Waves attractors in rotating fluids: a paradigm for ill-posed Cauchy problems

M. Rieutord; B. Georgeot; L. Valdettaro

doi:10.1103/physrevlett.85.4277

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Waves attractors in rotating fluids: a paradigm for ill-posed Cauchy problems

M. Rieutord·B. Georgeot·L. Valdettaro

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Abstract

In the limit of low viscosity, we show that the amplitude of the modes of oscillation of a rotating fluid, namely inertial modes, concentrate along an attractor formed by a periodic orbit of characteristics of the underlying hyperbolic Poincaré equation. The dynamics of characteristics is used to elaborate a scenario for the asymptotic behaviour of the eigenmodes and eigenspectrum in the physically relevant régime of very low viscosities which are out of reach numerically. This problem offers a canonical ill-posed Cauchy problem which has applications in other fields.

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M. Rieutord, B. Georgeot, L. Valdettaro. 2000-11-15. Waves attractors in rotating fluids: a paradigm for ill-posed Cauchy problems. https://doi.org/10.1103/physrevlett.85.4277

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