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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.

Wave Attractors in Rotating Fluids: A Paradigm for Ill-Posed Cauchy Problems