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Abstrakty
The fourth order nonlinear evolution equations are derived for a capillary-gravity wave packet for the case of resonant interaction with internal wave in the presence of a thin thermocline at a finite depth in deep water. These equations are used to make stability analysis of a uniform capillary-gravity wave train when resonance condition is satisfied. It is observed that for surface gravity waves the instability region expands with the decrease of thermocline depth. For surface capillary-gravity waves the growth rate of instability is much higher if the thermocline is formed at lower depth and for a fixed thermocline depth it increases with the increase of wave amplitude.
Rocznik
Tom
Strony
653--668
Opis fizyczny
Bibliogr. 19 poz., wykr.
Twórcy
autor
autor
- Department of Applied Mathematics University of Calcutta 92, Acharya Prafulla Chandra Road Kolkata-700009, INDIA, sdappmath@caluniv.ac.in
Bibliografia
- Bhattacharya S. and Das K.P.(1997): Fourth order nonlinear evolution equations for surface gravity waves in the presence of a thin thermocline. - J. Austral. Math. Soc. Ser., vol.B39, pp.214-229.
- Brinch-Nielsen U. 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.
- 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.
- Debsarma S. and Das K.P.(2002): Fourth order nonlinear evolution equations for gravity-capillary waves in the presence of a thin thermocline in deep water. - ANZIAM J., vol.43, pp.513-524.
- Dhar A.K. and Das K.P. (1993): Effect of capillarity on fourth-order nonlinear evolution equations for two Stokes wave trains in deep water. - J. Indian Inst. Sci., vol.73, pp.579.
- Dysthe K.B. (1979): Note on a modification to the nonlinear Schrodinger equation for application to deep water waves. - Proc. Roy. Soc. Lond, Ser., vol.A369, pp.105-114.
- Dysthe K.B. and Das K.P. (1981): Coupling between surface wave spectrum and an internal wave: modulational interaction. - J. Fluid Mech., vol.104, pp.483-503.
- Hara T. and Mei C.C. (1994) : Wind effects on nonlinear evolution of slowly varying gravity-capillary waves. - J. Fluid Mech., vol.267, pp.221-250.
- Funakoshi M. and Oikawa M. (1983): The resonant interaction between a long gravity wave and a surface gravity wave packet. - J. Phys. Soc. Japan, vol.52, pp.1982.
- Hasselman K.(1967): Nonlinear interactions treated by method of theoretical physics (with application to generation of waves by wind). - Proc. R. Soc. Lond., vol.A229, pp.77.
- Hogan S.J. (1985): Fourth order evolution equation for deep water gravity - capillary waves. - Proc. R. Soc. Lond., vol.A402, pp.359-372.
- Janssen P.A.E.M. (1983): On a fourth-order envelope 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.Superharmonics. - Proc. R. Soc. Lond., vol.A360, pp.471-488.
- Longuet-Higgins M.S.(1978b): The instabilities of gravity waves of finite amplitude in deep water II. Subharmonics. - Proc. R. Soc. Lond., vol.A360, pp.489-506.
- Ma Y.C. (1983): A study of resonant interaction between internal and surface waves based on a two layer fluid model. - Wave Motion, vol.5, pp.145.
- Olber D.J. and Herterich K. (1979): The special energy transfer from surface waves to internal waves. - J. Fluid Mech., vol.92, pp.349-379.
- Philips O.M. (1977): The Dynamics of Upper ocean. - Cambridge University Press.
- Rizk M.H. and Ko D.R.S. (1978): Interaction between small scale surface waves and large scale internal waves. - Phys. Fluids, vol.21, pp.1900-1907.
- Stiassnie M. (1984): Note on the modified nonlinear Schrödinger equation for deep water waves. - Wave Motion, vol.6, pp.431-433.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ2-0037-0025