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On the turbulent flow over a wavy boundary

Published online by Cambridge University Press:  29 March 2006

Russ E. Davis
Russ E. Davis
Affiliation:
Scripps Institution of Oceanography University of California, San Diego
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Abstract

Two hypotheses concerning the turbulent flow over an infinitesimal-amplitude travelling wave are investigated. One hypothesis, originally made by Miles, is that the wave does not affect the turbulence and therefore the turbulent Reynolds stresses are dependent only on height above the mean wave surface. Alternatively, the proposal that turbulent stresses are primarily dependent on height above the instantaneous wave surface is examined. Numerical solutions of the appropriate equations are compared with Stewart's recent experimental results and with the approximate solutions employed by Miles and others. No definite conclusion can be reached from comparison with experimental results since the predicted flows are quite sensitive to details of the mean velocity profile near the wave surface where no data was taken. It is found that the asymptotic results do not apply for the conditions investigated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 42 , Issue 4 , 30 July 1970 , pp. 721 - 731
Copyright
© 1970 Cambridge University Press

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References

Benjamin, T. B. 1959 Shearing flow over a wavy boundary. J. Fluid Mech. 6, 161.Google Scholar
Davis, R. E. 1969 On the high Reynolds number flow over a wavy boundary. J. Fluid Mech. 36, 337.Google Scholar
Hinze, J. O. 1959 Turbulence. New York: McGraw-Hill.
Kaplan, R. E. 1964 Solution of the Orr-Sommerfeld equation for laminar boundary layer flow over compliant boundaries. Cambridge Aeroelastic and Structures Research Laboratory ASRL — TR–116–1, Mass. Inst. Tech.
Lin, C. C. 1955 The Theory of Hydrodynamic Stability. Cambridge University Press.
Longuet-Higgins, M. S. 1969 On the action of a variable stress at the surface of water waves. Phys. Fluids, 12, 737.Google Scholar
Miles, J. W. 1957 On the generation of surface waves by shear flows. J. Fluid Mech. 3, 185.Google Scholar
Miles, J. W. 1959 On the generation of surface waves by shear flows, Part 2. J. Fluid Mech. 6, 568.Google Scholar
Miles, J. W. 1967 On the generation of surface waves by shear flows, Part 5. J. Fluid Mech. 30, 163.Google Scholar
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.
Stewart, R. H. 1969 Laboratory studies of the velocity field over water waves. J. Fluid Mech. 42, 733.Google Scholar