January 29: Ed Spiegel, Department of Astronomy, Columbia University
Continuum Equations for Rarefied Gases
Kirchhoff, who participated in the early development of the fluid dynamical equations, used them to
study the propagation of sound waves. In the last century, it was found that his results for the phase speeds
and the damping lengths of the waves were in disagreement with experiment when the mean free paths of the
particles in the gas were longer than the acoustic wave
lengths.
One source of this problem is in the iterative character of the usual ChapmanEnskog development. For long mean free paths, the NavierStokes
equations may be repaired by excluding the iterative
steps from their derivation. The fluid equations that
are then extracted from kinetic theory lead to phase
speeds that agree with experimental results. But the
damping lengths from the augmented NS equations
still do not agree with those from experiments in the
long mean free path limit. Rational approximations
of the leading terms of the fluid equations may repair
this fault, provided attention is paid to the role of time
in the dynamics, but they lack a certain inevitability.
The acausal aspect of the standard fluid equations also
is removed. Astrophysical topics that may relate to
these issues will be mentioned as time permits.
