Volume 96, Number 2, October 2011
|Number of page(s)||5|
|Section||Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics|
|Published online||06 October 2011|
Warm turbulence in the Boltzmann equation
Dipartimento di Fisica Generale, Università degli Studi di Torino - Via Pietro Giuria 1, 10125 Torino, Italy, EU
2 INFN, Sezione di Torino - Via Pietro Giuria 1, 10125 Torino, Italy, EU
3 Mathematics Institute, The University of Warwick - Coventry, CV4-7AL, UK, EU
4 Dipartimento di Energetica, Politecnico di Torino - Corso Duca degli Abruzzi 24, 10129 Torino, Italy, EU
Accepted: 2 September 2011
We study the single-particle distributions of three-dimensional hard-sphere gas described by the Boltzmann equation. We focus on the steady homogeneous isotropic solutions in thermodynamically open conditions, i.e. in the presence of forcing and dissipation. We observe a nonequilibrium steady-state solution characterized by a warm turbulence, that is an energy and particle cascade superimposed on the Maxwell-Boltzmann distribution. We use a dimensional analysis approach to relate the thermodynamic quantities of the steady state with the characteristics of the forcing and dissipation terms. In particular, we present an analytical prediction for the temperature of the system which we show to be dependent only on the forcing and dissipative scales. Numerical simulations of the Boltzmann equation support our analytical predictions.
PACS: 47.27.Gs – Isotropic turbulence; homogeneous turbulence / 05.70.Ln – Nonequilibrium and irreversible thermodynamics / 47.70.Nd – Nonequilibrium gas dynamics
© EPLA, 2011
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