Viscous effects on evolution of stokes waves

Philip L.F. Liu

doi:10.1061/(ASCE)0733-950X(1986)112:1(55)

Viscous effects on evolution of stokes waves

Philip L.F. Liu

Department of Hydraulic and Ocean Engineering

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

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 Schrodinger 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.

Original language	English
Pages (from-to)	55-63
Number of pages	9
Journal	Journal of Waterway, Port, Coastal and Ocean Engineering
Volume	112
Issue number	1
DOIs	https://doi.org/10.1061/(ASCE)0733-950X(1986)112:1(55)
Publication status	Published - 1986 Jan

All Science Journal Classification (ASJC) codes

Civil and Structural Engineering
Water Science and Technology
Ocean Engineering

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10.1061/(ASCE)0733-950X(1986)112:1(55)

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AB - 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 Schrodinger 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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Viscous effects on evolution of stokes waves

Abstract

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