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Instability waves on the air–sea interface

Published online by Cambridge University Press:  26 April 2006

G. H. Wheless  and
G. T. Csanady
G. H. Wheless
Affiliation:
Center for Coastal Physical Oceanography, Old Dominion University, Norfolk, VA 23529-0276, USA
G. T. Csanady
Affiliation:
Center for Coastal Physical Oceanography, Old Dominion University, Norfolk, VA 23529-0276, USA
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Abstract

We used a compound matrix method to integrate the Orr–Sommerfeld equation in an investigation of short instability waves (λ < 6 cm) on the coupled shear flow at the air–sea interface under suddenly imposed wind (a gust model). The method is robust and fast, so that the effects of external variables on growth rate could easily be explored. As expected from past theoretical studies, the growth rate proved sensitive to air and water viscosity, and to the curvature of the air velocity profile very close to the interface. Surface tension had less influence, growth rate increasing somewhat with decreasing surface tension. Maximum growth rate and minimum wave speed nearly coincided for some combinations of fluid properties, but not for others.

The most important new finding is that, contrary to some past order of magnitude estimates made on theoretical grounds, the eigenfunctions at these short wavelengths are confined to a distance of the order of the viscous wave boundary-layer thickness from the interface. Correspondingly, the perturbation vorticity is high, the streamwise surface velocity perturbation in typical cases being five times the orbital velocity of free waves on an undisturbed water surface. The instability waves should therefore be thought of as fundamentally different flow structures from free waves: given their high vorticity, they are akin to incipient turbulent eddies. They may also be expected to break at a much lower steepness than free waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 248 , March 1993 , pp. 363 - 381
Copyright
© 1993 Cambridge University Press

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