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06:42
Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Wave attractors in rotating fluids: A paradigm for ill-posed cauchy problems
Rieutord1, Georgeot, Valdettaro
1Observatoire Midi-Pyrenees, 14 avenue Edouard Belin, F-31400 Toulouse, France and Institut Universitaire de France.
Physical Review Letters
|November 4, 2000
Summary
In low viscosity fluids, inertial modes concentrate on a periodic orbit attractor. This reveals the asymptotic behavior of fluid oscillations in challenging numerical regimes.
Area of Science:
- Fluid dynamics
- Asymptotic analysis
- Numerical analysis
Background:
- Rotating fluids exhibit complex oscillation modes, known as inertial modes.
- Understanding the behavior of these modes at very low viscosities is crucial but numerically challenging.
- The underlying dynamics are related to hyperbolic partial differential equations.
Purpose of the Study:
- To investigate the asymptotic behavior of inertial modes in rotating fluids at low viscosities.
- To identify the mathematical structures governing the concentration of oscillation amplitudes.
- To provide a framework for analyzing ill-posed problems with applications beyond fluid dynamics.
Main Methods:
- Analysis in the limit of low viscosity.
- Identification of an attractor formed by a periodic orbit of characteristics.
- Utilizing the dynamics of characteristics to predict asymptotic behavior.
Main Results:
- Inertial mode amplitudes concentrate along a periodic orbit attractor.
- A scenario for the asymptotic behavior of eigenmodes and eigenspectra is elaborated.
- The findings are relevant for regimes beyond current numerical reach.
Conclusions:
- The study elucidates the behavior of inertial modes in low-viscosity rotating fluids.
- The identified attractor provides a novel perspective on fluid oscillation dynamics.
- The methodology addresses a canonical ill-posed Cauchy problem with broad applicability.
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