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Frame-indifferent kinetic theory

Published online by Cambridge University Press:  20 April 2006

L. C. Woods
L. C. Woods
Affiliation:
Mathematical Institute, University of Oxford
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Abstract

The second-order transport terms in a monatomic gas, originally derived by Burnett from Boltzmann's equation via the Chapman–Enskog iteration, have the curious property of being dependent on the observer's reference frame. However, frame-indifference has long been accepted as an essential property of constitutive equations in continuum mechanics. Various attempts have been made to find errors in the kinetic theory, but these have been countered by physical accounts of the framedependent terms that are independent of the Chapman–Enskog theory.

It is shown in this paper that both the Chapman–Enskog theory and the physical models are based on an inappropriate definition of the peculiar velocity. The Chapman–Enskog theory is easily corrected, and the result is a kinetic theory in harmony with the principle of material frame-indifference. A brief survey of the debate on this topic is presented, and corrected expressions are given for the Burnett terms.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 136 , November 1983 , pp. 423 - 433
Copyright
© 1983 Cambridge University Press

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