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Finite-amplitude acoustic-gravity waves: exact solutions

Published online by Cambridge University Press:  12 February 2015

Oleg A. Godin
Oleg A. Godin*
Affiliation:
Cooperative Institute for Research in Environmental Sciences, University of Colorado at Boulder, Boulder, CO 80309-0216, USA NOAA/Earth System Research Laboratory, Physical Sciences Division, Boulder, CO 80305-3328, USA
*
†Email address for correspondence: [email protected]
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Abstract

We consider strongly nonlinear waves in fluids in a uniform gravity field, and demonstrate that an incompressible wave motion, in which pressure remains constant in each fluid parcel, is supported by compressible fluids with free and rigid boundaries. We present exact analytic solutions of nonlinear hydrodynamics equations which describe the incompressible wave motion. The solutions provide an extension of the Gerstner wave in an incompressible fluid with a free boundary to waves in compressible three-dimensionally inhomogeneous moving fluids such as oceans and planetary atmospheres.

JFM classification

Compressible Flows: Compressible Flows Mathematical Foundations: General fluid mechanics Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 767 , 25 March 2015 , pp. 52 - 64
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Copyright
© 2015 Cambridge University Press 

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