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

M. Rieutord (1) , Bertrand Georgeot (2) , L. Valdettaro

1 UMS 831 - Services communs OMP
2 GPT-LPQ - Groupe de Physique Théorique (LPQ)

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.

Domaines: Formation de Structures et Solitons [nlin.PS]; Cosmologie et astrophysique extra-galactique [astro-ph.CO]; Cosmologie et astrophysique extra-galactique [astro-ph.CO]; Autre [cond-mat.other]; Relativité Générale et Cosmologie Quantique [gr-qc]; Dynamique des Fluides [physics.flu-dyn]

M. Rieutord, Bertrand Georgeot, L. Valdettaro. Waves attractors in rotating fluids: a paradigm for ill-posed Cauchy problems. Physical Review Letters, 2000, 85, pp.4277. ⟨10.1103/PhysRevLett.85.4277⟩. ⟨hal-00124360⟩