Proment, David, Onorato, Miguel, Asinari, Pietro and Nazarenko, Sergey (2012) Warm cascade states in a forced-dissipated Boltzmann gas of hard spheres. Physica D: Nonlinear Phenomena, Volume 241 (Number 5). pp. 600-615. doi:10.1016/j.physd.2011.11.019

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Abstract

We study the homogeneous isotropic Boltzmann equation for an open system. For the case of a hard spheres gas, we look for nonequilibrium steady solutions in the presence of forcing and dissipation. Using the language of weak turbulence theory, we analyze the possibility of observing the Kolmogorov–Zakharov steady distributions, i.e. solutions characterized by constant fluxes of conserved quantities. We derive a differential approximation model and we find that the expected nonequilibrium steady solutions have always the form of warm cascades. We propose an analytical prediction for the relation between the forcing and dissipation and the thermodynamic quantities of the system. Specifically, we find that the temperature of the system is independent of the forcing amplitude and determined only by the forcing and dissipation scales. Finally, we perform direct numerical simulations of the Boltzmann equation finding consistent results with our theoretical predictions.

Item Type:	Journal Article
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	Physica D: Nonlinear Phenomena
Publisher:	Elsevier BV
ISSN:	0167-2789
Official Date:	1 March 2012
Dates:	Date Event 1 March 2012 Published
Volume:	Volume 241
Number:	Number 5
Page Range:	pp. 600-615
DOI:	10.1016/j.physd.2011.11.019
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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