Breakdown of the Sonine expansion for the velocity distribution of granular gases

• Published in: Europhysics letters Vol. 74; no. 3; pp. 424 - 430
• Main Authors: Brilliantov, N. V, Pöschel, T
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.05.2006; EDP Sciences
• Subjects: 05.20.-y; 45.70.-n; 51.10.+y
• ISSN: 0295-5075; 1286-4854
• DOI: 10.1209/epl/i2005-10555-6

The velocity distribution of a granular gas is analyzed in terms of the Sonine polynomials expansion. We derive an analytical expression for the third Sonine coefficient a3. In contrast to frequently used assumptions this coefficient is of the same order of magnitude as the second Sonine coefficient a2. For small inelasticity the theoretical result is in good agreement with numerical simulations. The next-order Sonine coefficients a4, a5 and a6 are determined numerically. While these coefficients are negligible for small dissipation, their magnitude grows rapidly with increasing inelasticity for $0< \varepsilon \lesssim 0.6$. We conclude that this behavior of the Sonine coefficients manifests the breakdown of the Sonine polynomial expansion caused by the increasing impact of the overpopulated high-energy tail of the distribution function.