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Nonlinear waves in compacting media

Published online by Cambridge University Press:  21 April 2006

Victor Barcilon  and
Frank M. Richter
Victor Barcilon
Affiliation:
Department of the Geophysical Sciences, The University of Chicago, Chicago, IL 60637, USA
Frank M. Richter
Affiliation:
Department of the Geophysical Sciences, The University of Chicago, Chicago, IL 60637, USA
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Abstract

An investigation of the mathematical model of a compacting medium proposed by McKenzie (1984) for the purpose of understanding the migration and segregation of melts in the Earth is presented. The numerical observation that the governing equations admit solutions in the form of nonlinear one-dimensional waves of permanent shape is confirmed analytically. The properties of these solitary waves are presented, namely phase speed as a function of melt content, nonlinear interaction and conservation quantities. The information at hand suggests that these waves are not solitons.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 164 , March 1986 , pp. 429 - 448
Copyright
© 1986 Cambridge University Press

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