TECHNICAL PAPERS
Jan 1, 1986

Viscous Effects on Evolution of Stokes Waves

Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 112, Issue 1

Abstract

The effects of laminar viscosity on the evolution of a steady Stokes wave train are investigated by employing a boundary‐layer method. It is assumed that the nonlinearity of the second order in the wave slope, 0(ka)2, is in the same order of magnitude as the viscous effect; i.e., 0(ka)2=0(kδ), where δ=v/2ω=the Stokes boundary layer thickness. A nonlinear Schrödinger equation with a dissipation term is derived as the governing equation for the wave envelope. It is shown that the viscosity not only reduces the wave amplitude but also causes a phase shift in the same order of magnitude.

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References

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Booij, N., “Gravity waves on water with non‐uniform depth and currents,” Report 81‐1, Department of Civil Engineering, Delft Univ. of Technology, Delft, The Netherlands, 1981.
2.
Chu, V. H., and Mei, C. C., “On slowly‐varying Stokes waves,” Journal of Fluid Mechanics, Vol. 41, 1970, pp. 873–887.
3.
Dalrymple, R. A., Kirby, J. T., and Hwang, P. A., “Wave diffraction due to areas of energy dissipation,” Journal of the Waterway, Port, Coastal, and Ocean Engineering Division, ASCE, Vol. 110, 1980, pp. 67–79.
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Kirby, J. T., and Dalrymple, R. A., “A parabolic equation for the combined refraction‐diffraction of Stokes waves by mildly varying topography,” Journal of Fluid Mechanics, Vol. 136, 1983, pp. 453–466.
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Liu, P. L.‐F., and Tsay, T.‐K., “Refraction‐diffraction model for weakly nonlinear water waves,” Journal of Fluid Mechanics, Vol. 141, 1984, pp. 265–274.
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Mei, C. C., and Liu, P. L.‐F., “The damping of surface gravity waves in a bounded liquid,” Journal of Fluid Mechanics, Vol. 59, 1973, pp. 239–256.
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Whalin, R. W., “The limit of applicability of linear wave refraction theory in a convergence zone,” Research Report H‐71‐3, US Army Corps of Engineers, Waterways Experiment Station, Vicksburg, MS, 1971.
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Yue, D. K. P., and Mei, C. C., “Forward diffraction of Stokes waves by a thin wedge,” Journal of Fluid Mechanics, Vol. 99, 1980, pp. 33–52.

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Go to Journal of Waterway, Port, Coastal, and Ocean Engineering
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 112Issue 1January 1986
Pages: 55 - 63

History

Published online: Jan 1, 1986
Published in print: Jan 1986

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Authors

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Philip L.‐F. Liu, M. ASCE
Prof. and Assoc. Dir., School of Civ. and Environmental Engrg., Cornell Univ., Ithaca, NY 14853

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