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Dissipative waves in fluids having both positive and negative nonlinearity

Published online by Cambridge University Press:  21 April 2006

M. S. Cramer ,
A. Kluwick ,
L. T. Watson  and
W. Pelz
M. S. Cramer
Affiliation:
Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA
A. Kluwick
Affiliation:
Institut für Stoömungslehre und Wärmeübertragung, Technical University of Vienna, Wiedner Hauptstr. 7, A-1040 Vienna, Austria
L. T. Watson
Affiliation:
Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA
W. Pelz
Affiliation:
Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA Present address: Department of Mathematical Sciences, University of Akron, Akron, OH 44325, USA.
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Abstract

We examine weakly dissipative, weakly nonlinear waves in which the fundamental derivative $\overline{\Gamma}$ changes sign. The undisturbed state is taken to be at rest, uniform and in the vicinity of the $\overline{\Gamma} = 0$ locus. The cubic Burgers equation governing these waves is solved numerically; the resultant solutions are compared and contrasted to those of the inviscid theory. Further results include the presentation of a natural scaling law and inviscid solutions not reported elsewhere.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 169 , August 1986 , pp. 323 - 336
Copyright
© 1986 Cambridge University Press

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