Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-28T07:52:27.485Z Has data issue: false hasContentIssue false
  • English
  • Français

The growth of gravity-capillary waves in a coupled shear flow

Published online by Cambridge University Press:  11 April 2006

G. R. Valenzuela
G. R. Valenzuela
Affiliation:
Ocean Sciences Division, Naval Research Laboratory, Washington D.C. 20375
Get access Rights & Permissions [Opens in a new window]

Abstract

The growth rates and phase speeds of gravity-capillary wind waves are investigated through numerical solution of a linear, viscous, coupled, shear-flow perturbation model. Numerical results are obtained by transforming the boundary-value problem of a perturbed mean laminar shear flow into a matrix-eigenvalue problem using standard finite-difference methods.

Detailed calculations are performed for a basic state composed of a logarithmic-linear mean flow profile in the air and a linear-logarithmic mean flow profile in the water. We exclude turbulent Reynolds stresses. Calculated growth rates show excellent agreement with corresponding experimental growth rates. This implies that the initial growth of gravity-capillary wind waves is almost certainly due to the instability of the coupled laminar shear flow in the air and water.

The investigation also demonstrates that the shear flow in the water cannot be ignored in wave growth studies, since the usual 3-4%, highly sheared, wind-induced surface drift produces a significant increase in the growth of wind-generated gravity-capillary waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 76 , Issue 2 , 28 July 1976 , pp. 229 - 250
Copyright
© 1976 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Benjamin, T. B. 1959 J. Fluid Mech. 6, 161–205.
Gottifredi, J. C. & Jameson, G. J. 1970 Proc. Roy. Soc. A 319, 373–397.
Hasselmann, K., Ross, D. B., Müller, P. & Sell, W. 1976 J. Phys. Ocean. (to be published).
Hasselmann, K. et al. 1973 Dsche Hydrogr. Z., Suppl. A (8$), no. 12.
Hidy, G. M. & Plate, E. J. 1966 J. Fluid Mech 26, 651–687.
Hughes, T. H. 1972 Phys. Fluids, 15, 725–728.
Jordinson, R. 1970 J. Fluid Mech 43, 801–811.
Keller, W. C., Larson, T. R. & Wright, J. W. 1974 Radio Sci 9, 1091–1100.
Kurtz, E. F. & Crandall, S. H. 1962 J. Math. Phys. 41, 264–279.
Larson, T. R. & Wright, J. W. 1975 J. Fluid Mech 70, 417–436.
Miles, J. W. 1957 J. Fluid Mech 3, 185–204.
Miles, J. W. 1959 J. Fluid Mech 6, 568–582.
Miles, J. W. 1962a J. Fluid Mech 13, 427–432.
Miles, J. W. 1962b J. Fluid Mech 13, 433–448.
Mitsuyasu, H. & Honda, T. 1975 Res. Inst. Appl. Mech., Kyushu Univ., Japan, no. 22, pp. 327–355.
Osborne, R. 1967 SIAM J. Appl. Math 15, 539–557.
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.
Shemdin, O. H. 1972 J. Phys. Ocean 2, 411–419.
Stewart, R. H. 1970 J. Fluid Mech 42, 733–754.
Thomas, L. H. 1953 Phys. Rev 91, 780–783.
Wilson, W. S., Banner, M. L., Flower, R. J., Michael, J. A. & Wilson, D. G. 1973 J. Fluid Mech 58, 435–460.
Wright, J. W. & Keller, W. C. 1971 Phys Fluids, 14, 466–474.
Wu, J. 1975 J. Fluid Mech 68, 49–70.