Waves attractors in rotating fluids: a paradigm for ill-posed Cauchy problems
Fluid Dynamics
2008-11-26 v1 Astrophysics
Condensed Matter
General Relativity and Quantum Cosmology
Pattern Formation and Solitons
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 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.
Cite
@article{arxiv.physics/0011031,
title = {Waves attractors in rotating fluids: a paradigm for ill-posed Cauchy problems},
author = {M. Rieutord and B. Georgeot and L. Valdettaro},
journal= {arXiv preprint arXiv:physics/0011031},
year = {2008}
}
Comments
4 pages, 5 fig