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An exact form of Lilley's equation with a velocity quadrupole/temperature dipole source term

Published online by Cambridge University Press:  25 September 2001

M. E. GOLDSTEIN
M. E. GOLDSTEIN
Affiliation:
National Aeronautics and Space Administration, Glenn Research Center, Cleveland, Ohio 44135, USA
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Abstract

There have been several attempts to introduce approximations into the exact form of Lilley's equation in order to express the source term as the sum of a quadrupole whose strength is quadratic in the fluctuating velocities and a dipole whose strength is proportional to the temperature fluctuations. The purpose of this note is to show that it is possible to choose the dependent (i.e. the pressure) variable so that this type of result can be derived directly from the Euler equations without introducing any additional approximations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 443 , 25 September 2001 , pp. 231 - 236
Copyright
© 2001 Cambridge University Press

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