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The role of drift mass in the kinetic energy and momentum of periodic water waves and sound waves

Published online by Cambridge University Press:  21 May 2009

CHIA-SHUN YIH
CHIA-SHUN YIH
Affiliation:
The University of Michigan, Ann Arbor, Michigan 48109-2125, USA
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Abstract

For two-dimensional periodic water waves or sound waves, the kinetic energy per wavelength is ½mdc2, and the momentum per wavelength is ±mdc, where c is the wave velocity, and md is the drift mass per wavelength. These results also hold for three-dimensional periodic waves, for which the kinetic energy, momentum, and drift mass are all for one wave cell, the area of which is the product of the wavelengths in two perpendicular directions.

The results obtained are rigorous, and not restricted to linear waves or even to nonlinear symmetric waves. For linear water waves, in particular, the kinetic energy can be shown to be equal to the sum of the potential energy and the surface energy (due to surface tension), so that the total energy E is twice the kinetic energy, and

formula here

McIntyre's (1981) contention that wave momentum is a myth is discussed at length for both water waves and sound waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 331 , 25 January 1997 , pp. 429 - 438
Copyright
© 1997 Cambridge University Press

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