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Fluid Dynamics
Erschienen in: Fluid Dynamics 1/2023

01.02.2023

A Nonlinear Schrödinger Equation for Gravity-Capillary Waves on Deep Water with Constant Vorticity

verfasst von: M. I. Shishina

Erschienen in: Fluid Dynamics | Ausgabe 1/2023

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Abstract

The surface gravity-capillary waves on deep water with constant vorticity in the region bounded by the free surface and the infinitely deep plane bottom are considered. A nonlinear Schrödinger equation is derived from a system of exact nonlinear integro-differential equations in conformal variables written in the implicit form taking into account surface tension. In deriving the nonlinear Schrödinger equation, the role of the mean flow is taken into account. The nonlinear Schrödinger equation is investigated for modulation instability. A soliton solution of the nonlinear Schrödinger equation that represents a soliton of the “ninth wave” type is obtained.
Vorheriger Artikel Numerical Simulation of Turbulent Flow Control at Pipe Inlet to Advance Flow Relaminarization
Nächster Artikel Effect of Confinement of Flow by Side Walls on the Cross Flow past a Circular Cylinder at Moderate Reynolds Numbers

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Literatur
1.
Zakharov, V.E., Stability of periodic waves of finite amplitude on the surface of a deep fluid, Zh. Prikl. Mekh. Tekh. Fiz., 1968, vol. 9, no. 2, pp. 86–94.
2.
Davey, A., The propagation of a weakly nonlinear wave, J. Fluid Mech., 1972, vol. 53, pp. 769–781.ADSCrossRefMATH
3.
Hasimoto, H., and Ono, H., Nonlinear modulation of gravity waves, J. Phys. Soc. Japan, 1972, vol. 33, pp. 805–811.ADSCrossRef
4.
Yuen, H.C. and Lake, B.M., Nonlinear deep water waves: Theory and experiment, Phys. Fluids, 1975, vol. 18, pp. 956–960.ADSCrossRefMATH
5.
Johnson, R.S., On the modulation of water waves on shear flows, Proc. R. Soc. Lond. A., 1976, vol. 347, pp. 537–546.ADSCrossRefMATH
6.
Li, J.C., Hui, W.H., and Donelan, M.A., Effects of velocity shear on the stability of surface deep water wave trains, in: Nonlinear Water Waves, ed. by K. Horikawa and H. Maruo, Springer, 1987, pp. 213–220.
7.
Oikawa, M., Chow, K., and Benney, D.J., The propagation of nonlinear wave packets in a shear flow with a free surface, Stud. Appl. Math., 1987, vol. 76, pp. 69–92.MathSciNetCrossRefMATH
8.
9.
Thomas, R., Kharif, C., and Manna, M., A nonlinear Schrödinger equation for water waves on finite depth with constant vorticity, Phys. Fluids, 2012, vol. 24, p. 127102.
10.
Simmen, J.A. and Saffman, P.G., Steady deep-water waves on a linear shear current, Stud. Appl. Maths., 1985, vol. 73, pp. 35–57.MathSciNetCrossRefMATH
11.
Hsu, H.C., Kharif, C., Abid, M., and Chen, Y.Y., A nonlinear Schrödinger equation for gravity–capillary water waves on arbitrary depth with constant vorticity. Part 1, J. Fluid. Mech., 2018, vol. 854, pp. 146–163.ADSMathSciNetCrossRefMATH
12.
13.
Ovsyannikov, L.V., On the justification of the shallow water theory, in: Dynamics of Continuum, Proceedings of the Siberian Branch of the Academy of Sciences of the USSR, Novosibirsk: Institute of Hydrodynamics, 1973, no. 15, pp. 104–125.
14.
Dyachenko, A.I., Kuznetsov, E.A., Spector, M.D., and Zakharov, V.E., Analytical description of the free surface dynamics of an ideal fluid (canonical formalism and conformal mapping), Phys. Lett. A, 1996, vol. 221, nos. 1–2, pp. 73–79.ADSCrossRef
15.
Dyachenko, A.I., Zakharov, V.E., and Kuznetsov, E.A., Nonlinear dynamics of the free surface of an ideal fluid, Plasma Phys. Reports, 1996, vol. 22, no. 10, pp. 829–840.ADS
16.
Dyachenko, A.I., On the dynamics of an ideal fluid with a free surface, Dokl. Math., 2001, vol. 63, no. 1, pp. 115–117.
17.
Zakharov, V.E., Dyachenko, A.I., Vasilyev, O.A., New method for numerical simulation of a nonstationary potential flow of incompressible fluid with a free surface, Eur. J. Mech. B Fluids, 2002, vol. 21, pp. 283–291.MathSciNetCrossRefMATH
18.
Chalikov, D. and Sheinin, D., Numerical modeling of surface waves based on principal equations of potential wave dynamics, in: Technical Note. NOAA/NCEP/OMB, 1996, p. 54.
19.
Chalikov, D. and Sheinin, D., Modeling of extreme waves based on equations of potential flow with a free surface, J. Comp. Phys., 2005, vol. 210, pp. 247–273.ADSMathSciNetCrossRefMATH
20.
Ruban, V.P., Water waves over a time-dependent bottom: Exact description for 2D potential flows, Phys. Let. A, 2005, vol. 340, nos. 1–4, pp. 194–200.ADSMathSciNetCrossRefMATH
21.
Shishina, M.I., Steady surface gravity waves on a constant vorticity flow free surface, Processes in Geomedia, 2016, vol. 8, Special issue, pp. 71–77.
22.
Ruban, V.P., Explicit equations for two-dimensional water waves with constant vorticity, Phys. Rev. E, 2008, vol. 77, p. 037302.
Metadaten
Titel
A Nonlinear Schrödinger Equation for Gravity-Capillary Waves on Deep Water with Constant Vorticity
verfasst von
M. I. Shishina
Publikationsdatum
01.02.2023
Verlag
Pleiades Publishing
Erschienen in
Fluid Dynamics / Ausgabe 1/2023
Print ISSN: 0015-4628
Elektronische ISSN: 1573-8507
DOI
https://doi.org/10.1134/S0015462822601851

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