Geodesic
Nonlinear Stokes waves on the surface of low-viscosity fluid
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2011), pp. 112-122 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {2011},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2011_2_a7/}
}
TY  - JOUR
AU  - V. A. Barinov
AU  - K. Yu. Basinsky
TI  - Nonlinear Stokes waves on the surface of low-viscosity fluid
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2011
SP  - 112
EP  - 122
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VUU_2011_2_a7/
LA  - ru
ID  - VUU_2011_2_a7
ER  - 
%0 Journal Article
%A V. A. Barinov
%A K. Yu. Basinsky
%T Nonlinear Stokes waves on the surface of low-viscosity fluid
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2011
%P 112-122
%N 2
%U http://geodesic.mathdoc.fr/item/VUU_2011_2_a7/
%G ru
%F VUU_2011_2_a7
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/

[1] Stokes G. G., “On the theory of oscillatory waves”, Math. And Physic. Papers, 1 (1880), 197–229 | DOI

[2] Sretenskii L. N., Teoriya volnovykh dvizhenii zhidkosti, Nauka, M., 1977, 816 pp.

[3] Aleshkov Yu. Z., Teoriya voln na poverkhnosti tyazheloi zhidkosti, Izd-vo Leningr. un-ta, L., 1981, 196 pp. | MR | Zbl

[4] Barinov V. A., “Rasprostranenie voln po svobodnoi poverkhnosti vyazkoi zhidkosti”, Vestn. S.-Peterb. un-ta. Ser. 10, 2010, no. 2, 18–31

[5] Barinov V. A., Basinskii K. Yu., “Vliyanie vyazkosti zhidkosti na rasprostranenie poverkhnostnykh voln”, Tr. 10-i Vseross. konf. “Prikladnye tekhnologii gidroakustiki i gidrofiziki”, Nauka, SPb., 2010, 205–208

[6] Basinskii K. Yu., “Nelineinye volny na poverkhnosti slabovyazkoi zhidkosti”, Sb. tr. 3-i Region. konf. “Sovremen. problemy matemat. i inform. modelirovaniya”, Izd-vo “Vektor Buk”, Tyumen, 2010, 32–36

[7] Barinov V. A., Butakova N. N., “Nelineinaya zadacha o poverkhnostnykh volnakh na dvukhfaznoi smesi”, Zhurn. vychislit. matem. i matem. fiz., 43:12 (2003), 1870–1883 | MR | Zbl

[8] Joseph D. D., Wang J., “The dissipation approximation and viscous potential flow”, J. Fluid Mech., 505 (2004), 365–377 | DOI | MR | Zbl