Stability of small but finite amplitude interfacial capillary gravity waves for perturbations in two horizontal directions

• Autorzy: Majumder D. P. , Dhar A. K.
• Języki publikacji: EN

Abstrakty

EN

By exact numerical computation Yuen (1984) obtained regions of type-I instability for waves propagating at the interface of two superposed fluids of infinite thickness in which the upper fluid has a constant streaming velocity. In the present paper it is shown that the long wavelength part of these instability regions can be obtained analytically from a fourth order nonlinear evolution equation for small but finite amplitude interfacial capillary gravity waves in the presence of air flowing over water.

Słowa kluczowe

EN

nonlinear evolution equation; capillary-gravity wave; instability

PL

nieliniowe równania ewolucji; fala grawitacyjna; fala kapilarna; niestabilność

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2011
• Tom: Vol. 16, no 2
• Strony: 425--434
• Opis fizyczny: Bibliogr. 22 poz., wykr.

Twórcy

autor

Majumder D. P.

autor

Dhar A. K.

• Department of Mathematics Bengal Engineering and Science University, Shibpur P.O. Botanic Garden, Shibpur Howrah - 711103, West Bengal, INDIA,

Bibliografia

• Bliven L. F., Huang N.E. and Long S.R. (1986): Experimental study of the influence of wind on Benjamin- Feir sideband instability. - J. Fluid Mech., vol.162, pp.273.
• Das K.P. (1986): On evolution equations for a three dimensional surface gravity wave packet in a two layer fluid. - Wave Motion, vol.8, pp.191-204.
• Davey A. and Stewartson K. (1974): On three dimensional packets of surface waves. - Proc. R. Soc. Lond., A 338, pp.101-110.
• Dhar A.K. and Das K.P. (1991): Fourth order nonlinear evolution equation for two Stokes wave trains in deep water. - Phys. Fluids A3 (12), pp.3021-3026.
• Dhar A.K. and Das K.P. (1994): Stability analysis from fourth order evolution equation for small but finite amplitude interfacial waves in the presence of a basic current shear. - J. Austral. Math. Soc. vol. ser. B 35, pp.348-365.
• Dhar A.K. and Das K.P. (1999): A fourth order evolution equation for capillary gravity waves including the effects of wind input and shear in the water current. - Int. J. of Applied Mechanics and Engineering, vol.4, No.1, pp.5-24.
• Dhar A.K. and Das K.P. (2001): The effect of randomness on stability of surface gravity waves from fourth order nonlinear evolution equation. - Int. J. of Applied Mechanics and Engineering, vol.6, No.1, pp.11-34.
• Djordjevic V.D. and Redekopp L.G. (1977): On two dimensional packets of capillary gravity waves. - J. Fluid Mech., vol.79, pp.703-714.
• Dungey J.C. and Hui W.H. (1979): Nonlinear energy transfer in a narrow gravity-wave spectrum. - Proc. Roy. Soc. Lond. A 368, pp.239-265.
• Dysthe K.B. (1979): Note on a modification to the nonlinear Schrödinger equation for application to deep water waves. - Proc. R. Soc. Lond., vol.A 369, pp.105-114.
• Hogan S.J. (1985): The fourth order evolution equation for deep water gravity capillary waves. - Proc. R. Soc. Lond., vol.A 402, pp.359-372.
• Janssen P.A.E.M. (1983): On fourth order evolution equation for deep water waves. - J. Fluid. Mech., vol.126, pp.1-11.
• Longuet-Higgins M.S. (1978a): The instabilities of gravity waves of finite amplitude in deep water, I. Super Harmonics. Proc. R. Soc. Lond., vol.A 360, pp.471-488.
• Longuet-Higgins M.S. (1978b): The instabilities of gravity waves of finite amplitude in deep water, II. Sub Harmonics. Proc. R. Soc. Lond., vol.A 360, pp.489-506.
• Majumder D.P. and Dhar A.K. (2009): Stability analysis from fourth order evolution equation for deep water capillary-gravity waves in the presence of air flowing over water. - Int. J. of Applied Mechanics and Engineering, vol.14, No.2, pp.433-442.
• Majumder D.P. and Dhar A.K. (2009): Stability analysis from fourth order evolution equation for two Stokes wave trains in deep water in the presence of air flowing over water. - Int. J. of Applied Mechanics and Engineering, vol.14, No.4, pp.989-1008.
• McLean J.W., Ma Y.C., Martin D.U., Saffman P.G. and Yuen H.C. (1981): Three dimensional instability of finite amplitude water waves. - Phys. Rev. Lett. 46, pp.817-820.
• Nielsen U.B. and Jonsson I.G. (1986): Fourth order evolution equations and stability analysis for Stokes waves on arbitrary water depth. - Wave Motion, vol.8, pp.455-472.
• Pullin D.I. and Grimshaw R.H.J. (1986): Stability of finite amplitude interfacial waves. Part 3. The effect of basic current shear for one dimensional instabilities. - J. Fluid Mech., vol.172, pp.277-306.
• Stiassnie M. (1984): Note on the modified nonlinear Schrödinger equation for deep water waves. - Wave Motion, vol.6, pp.431-433.
• Yuen H.C. (1984): Non linear dynamics of interfacial waves. - Physica, vol.12D, pp.71-82.
• Zakharov V.E. (1968): Stability of periodic waves of finite amplitude on the surface of a deep fluid. - J. Appl. Mech. Tech. Phys., vol.2, pp.190-194.