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The interaction of large amplitude shallow-water waves with an ambient shear flow: non-critical flows

Published online by Cambridge University Press:  29 March 2006

P. A. Blythe ,
Y. Kazakia  and
E. Varley
P. A. Blythe
Affiliation:
Center for the Application of Mathematics, Lehigh University, Bethlehem, Pennsylvania
Y. Kazakia
Affiliation:
Center for the Application of Mathematics, Lehigh University, Bethlehem, Pennsylvania
E. Varley
Affiliation:
Center for the Application of Mathematics, Lehigh University, Bethlehem, Pennsylvania
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Abstract

This paper describes the behaviour of large amplitude, long gravity waves as they move over a horizontal bed into a region where the flow is steady but sheared in a vertical direction. A new class of exact solutions to the nonlinear hydraulic flow equations is derived. These solutions describe progressing waves and are sufficiently general to allow both the shape of the free surface at any instant and the shear profile of the undisturbed flow to be specified. The waves are examples of neutrally stable disturbances in the sense that they neither grow nor decay in amplitude, although, like simple waves on an unsheared flow, they can break.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 56 , Issue 2 , 28 November 1972 , pp. 241 - 255
Copyright
© 1972 Cambridge University Press

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References

Burns, J. C. 1953 Proc. Camb. Phil. Soc. 49, 695–706.
Freeman, N. C. & Johnson, R. S. 1970 J. Fluid Mech. 42, 401–409.
Phillips, W. A. 1957 J. Meteorology, 14, 184–185.
Stoker, J. J. 1957 Water Waves — The Mathematical Theory with Applications. Interscience.