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Eddy-viscosity and drag-law models for random ocean wave dissipation

Published online by Cambridge University Press:  26 April 2006

S. L. Weber
S. L. Weber
Affiliation:
Royal Netherlands Meteorological Institute, P.O. Box 201, 3730 AE De Bilt, The Netherlands
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Abstract

The spectral energy dissipation of finite-depth ocean waves, due to friction in the turbulent bottom boundary layer, is investigated using a formal parameterization of the turbulent stress. This formal parameterization is a generalization from both the eddy-viscosity model and the drag law. The eddy-viscosity model is linear in the random wave phase, whereas the drag law is nonlinear. The phase dependency of the stress is found to determine the form of the dissipation expression. A spectral eddy-viscosity model developed by the author, an eddy-viscosity model based on an ‘equivalent’ monochromatic wave given by Madsen et al. (1989), the drag law as applied by Hasselmann & Collins (1968) and an approximation to the Hasselmann & Collins expression given by Collins (1972) are discussed within the framework of the formal parameterization. Some examples of applications are given.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 232 , November 1991 , pp. 73 - 98
Copyright
© 1991 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover.
Bakker, W. T. & Doorn, Th. Van 1979 Near bottom velocities in waves with a current. In Proc. 16th Intl Conf. on Coastal Engng 1978, pp. 1394–1413. ASCE.
Beran, J. M. 1968 Statistical Continuum Theories. Interscience.
Bouws, E. & Komen, G. J. 1983 On the balance between growth and dissipation in an extreme depth-limited wind-sea in the southern North Sea. J. Phys. Oceanogr. 13, 1653–1658.Google Scholar
Christoffersen, J. B. & Jonsson, I. G. 1985 Bed friction in a combined current and wave motion. Ocean Engng 12, 387–423.Google Scholar
Collins, J. I. 1972 Prediction of shallow water spectra. J. Geophys. Res. 93 (Cl), 491–508.Google Scholar
Davies, A. G., Soulsby, R. L. & Kino, H. L. 1988 A numerical model of the combined wave and current bottom boundary layer. J. Geophys. Res. 93 (Cl), 491–508.Google Scholar
Dyer, K. R. & Soulsby, R. L. 1988 Sand transport on the continental shelf. Ann. Rev. Fluid Mech. 20, 295–324.Google Scholar
Grant, W. D. & Madsen, O. S. 1979 Combined wave and current interaction with a rough bottom. J. Geophys. Res. 84 (C4), 1797–1808.Google Scholar
Grant, W. D. & Madsen, O. S. 1982 Movable bed roughness in unsteady oscillatory flow. J. Geophys. Res. 87 (C1), 469–481.Google Scholar
Hasselmann, K. & Collins, J. I. 1968 Spectral dissipation of finite depth gravity waves due to turbulent bottom friction. J. Mar. Res. 26, 1–12.Google Scholar
Hino, M., Kashiwayanagi, M., Nakayama, A. & Hara, T. 1983 Experiments on the turbulence statistics and the structure of a reciprocating oscillatory flow. J. Fluid Mech. 131, 363–400.Google Scholar
Horikawa, K. & Watanabe, A. 1968 Laboratory study on oscillatory boundary layer flow. Coastal Engng Japan 11, 13–28.Google Scholar
Huntley, D. A. & Hazbn, D. G. 1988 Seabed stresses in combined wave and steady flow conditions on the Nova Scotia continental shelf: field measurements and predictions. J. Phys. Oceanogr. 19, 347–362.Google Scholar
Jonsson, I. G. 1980 A new approach to oscillatory rough turbulent boundary layers. Ocean Engng 7, 109–152.Google Scholar
Jonswap: Hasselmann, K., Barnett, T. P., Bouws, E., Carlson, H., Cartwright, D. E., Enke, K., Ewing, J. A., Gienapp, H., Hasselmann, D. E., Kruseman, P., Meerburg, A., Müller, P., Olbers, D. J., Richter, K., Sell, W. & Walden, H. 1973 Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Dtsch. Hydrogr. Z. A8 (12), 95.Google Scholar
Kajiura, K. 1968 A model of the bottom boundary layer in water waves. Bull. Earthquake Res. Inst. 46, 75–123.Google Scholar
Lavelle, J. W. & Mofjeld, H. 0. 1983 Effects of time-varying viscosity on oscillatory turbulent channel flow. J. Geophys. Res. 88 (C12), 7607–7616.Google Scholar
Longuet-Higgins, M. S. 1963 The effect of nonlinearities on statistical distributions in the theory of sea waves. J. Fluid Mech. 17, 459–480.Google Scholar
Madsen, O. S., Poon, Y.-K. & Graber, H. C. 1989 Spectral wave attenuation by bottom friction: theory. In Proc. 21st Conf. on Coastal Engng 1988, pp. 492–504. ASCE.
Nayfeh, A. H. 1973 Perturbation Methods. Wiley Interscience.
Rice, S. O. 1944 The mathematical analysis of random noise. Bell Syst. Tech. J. 23, 282–332.Google Scholar
Rice, S. O. 1945 The mathematical analysis of random noise. Bell Syst. Tech. J. 24, 46–156.Google Scholar
Schlichting, H. 1955 Boundary Layer Theory. McGraw Hill.
Shemdih, O., Hasselmann, K., Hsiao, S. V. & Herterich, K. 1978 Non-linear and linear bottom interaction effects in shallow water. In Turbulent Fluxes through the Sea Surface, Wave Dynamics and Prediction. NATO Conf. Ser. V, Vol. 1, pp. 647–665. Plenum.
Sleath, J. F. A. 1987 Turbulent oscillatory flow over rough beds. J. Fluid Mech. 182, 369–409.Google Scholar
Tennekes, H. & Lumely, J. L. 1972 A First Course in turbulence. The MIT Press.
Trowbridge, J. & Madsen, 0. S. 1984 Turbulent wave boundary layers, 1. Model formulation and first order solution. J. Geophys. Res. 89 (C5), 7989–7999.Google Scholar
Visseh, M. 1988 Energiedissipatie van zeegolven in de turbulente bodemgrenslaag. Sc.D. thesis. KNMI Tech. Rep. TR-104. De Bilt, The Netherlands (in Dutch).
Wamdi Group 1988 The WAM model — A third generation ocean wave prediction model. J. Phys. Oceanogr. 18, 1775–1810.Google Scholar
Weber, S. L. 1988 The energy balance of finite depth gravity waves. J. Geophys. Res. 93 (C4), 3601–3607.Google Scholar
Weber, S. L. 1989 Surface gravity waves and turbulent bottom friction. Ph.D. thesis, University of Utrecht.
Weber, S. L. 1991 Bottom friction for wind-sea and swell in extreme depth-limited situations. J. Phys. Oceanogr. 21, 149–172.Google Scholar
Wilson, K. C. 1989 Friction of wave-induced sheet flow. Coastal Engng 12, 371–379.Google Scholar