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The interaction of a contact discontinuity with sound waves according to the linearised Navier-Stokes equations

Published online by Cambridge University Press:  20 January 2009

W. M. Anderson
W. M. Anderson
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York
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Abstract

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The resolution of a small initial discontinuity in a gas is examined using the linearised Navier-Stokes equations. The smoothing of the resultant contact surface and sound waves due to dissipation results in small flows which interact. The problem is solved for arbitrary Prandtl number by using a Fourier transform in space and a Laplace transform in time. The Fourier transform is inverted exactly and the density perturbation is found as two asymptotic series valid for small dissipation near the contact surface and the sound waves respectively. The modifications to the structures of the contact surface and the sound waves are exhibited.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 17 , Issue 1 , June 1970 , pp. 37 - 46
Copyright
Copyright © Edinburgh Mathematical Society 1970

References

REFERENCES

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