Geodesic
Nonlinear Stokes waves on the surface of low-viscosity fluid
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2011), pp. 112-122

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The statements of nonlinear boundary-value problem for wave propagation over the free surface of low-viscosity fluid have been presented. Solution is found by the method of time-varying frequency, which is the Stokes' method generalized for the dissipative wave processes. The asymptotic solution up to the third-order approximation upon the wave parameter has been found. It is shown that the frequency and damping rate of the nonlinear wave tend in time to the values corresponding to a linear problem. Nonlinear trajectories of fluid particles and the expression for transfer velocity in a low-viscosity Stokes fluid have been defined.
Keywords: nonlinear surface waves
Mots-clés : viscous dissipation, dispersion relations. 
@article{VUU_2011_2_a7,
     author = {V. A. Barinov and K. Yu. Basinsky},
     title = {Nonlinear {Stokes} waves on the surface of low-viscosity fluid},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {112--122},
     publisher = {mathdoc},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2011_2_a7/}
}
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V. A. Barinov; K. Yu. Basinsky. Nonlinear Stokes waves on the surface of low-viscosity fluid. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2011), pp. 112-122. http://geodesic.mathdoc.fr/item/VUU_2011_2_a7/