Distribution function for large velocities of a two-dimensional gas under shear flow

Details Distribution function for large velocities of a two-dimensional gas under shear flow Distribution function for large velocities of a two-dimensional gas under shear flow

Sep 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996jsp....88.1165m&link_type=abstract

Journal of Statistical Physics, Volume 88, Issue 5-6, pp. 1165-1181

Physics

3

Boltzmann Equation, Velocity Moments, Maxwell Molecules, Uniform Shear Flow, Dsmc Method

Scientific paper

The high-velocity distribution of a two-dimensional dilute gas of Maxwell molecules under uniform shear flow is studied. First we analyze the shear-rate dependence of the eigenvalues governing the time evolution of the velocity moments derived from the Boltzmann equation. As in the three-dimensional case discussed by us previously, all the moments of degree k⩾4 diverge for shear rates larger than a critical value a {c/(k)}, which behaves for large k as a {c/(k)} ˜ k -1. This divergence is consistent with an algebraic tail of the form f( V) ˜ V -4-σ( a), where σ is a decreasing function of the shear rate. This expectation is confirmed by a Monte Carlo simulation of the Boltzmann equation far from equilibrium.

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