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

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

2000-11-15

arxiv.org/abs/physics/0011031v1

Phys.Rev.Lett.85:4277,2000

Physics

Fluid Dynamics

4 pages, 5 fig

Scientific paper

10.1103/PhysRevLett.85.4277

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 Poincar\'e equation. The dynamics of characteristics is used to elaborate a scenario for the asymptotic behaviour of the eigenmodes and eigenspectrum in the physically relevant r\'egime 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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