A short review is given of recent papers on the relaxation to (incompressible) absolute equilibrium. A new algorithm to construct absolute equilibrium of spectrally truncated compressible flows is described. The algorithm uses stochastic processes based on the Clebsch representation of the velocity field to generate density and velocity fields that follow by construction the absolute equilibrium stationary probability. The new method is shown to reproduce the well-known Gaussian results in the incompressible limit. The irrotational compressible absolute equilibrium case is characterized and the distribution is shown to be non-Gaussian. The high-temperature compressible spectra are found not to obey k2 scaling. Finally, oscillating behavior in constant-pressure variable-temperature relaxation is obtained, suggesting the presence of second sound.
|Number of pages
|International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
|Published - Oct 2009
Bibliographical noteFunding Information:
We acknowledge support from an ECOS/ CONICYT action and one of the authors (ET) is grateful to the Project ACT 15 of CONICYT, Chile. The computations were carried out at IDRIS (CNRS).
- Clebsch potentials
- Compressible fluids
- Truncated Euler equation