Wave attractors in rotating fluids: A paradigm for ill-posed cauchy problems
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 Poincare equation. The dynamics of characteristics is used to elaborate a scenario for the asymptotic behavior of the eigenmodes and eigenspectrum in the physically relevant regime 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.
Rieutord
M
Observatoire Midi-Pyrenees, 14 avenue Edouard Belin, F-31400 Toulouse, France and Institut Universitaire de France.
Georgeot
B
Valdettaro
L