Higher-order Korteweg-de Vries models for internal solitary waves in a stratified shear flow with a free surface

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Grimshaw , R. ; Pelinovsky , E. ; Poloukhina , O. (2002)
  • Publisher: European Geosciences Union (EGU)
  • Journal: (issn: 1607-7946, eissn: 1607-7946)
  • Related identifiers: doi: 10.5194/npg-9-221-2002
  • Subject: [ PHYS.ASTR.CO ] Physics [physics]/Astrophysics [astro-ph]/Cosmology and Extra-Galactic Astrophysics [astro-ph.CO] | [ SDU.STU ] Sciences of the Universe [physics]/Earth Sciences | [ SDU.ASTR ] Sciences of the Universe [physics]/Astrophysics [astro-ph]
    arxiv: Mathematics::Analysis of PDEs | Nonlinear Sciences::Pattern Formation and Solitons | Physics::Fluid Dynamics | Nonlinear Sciences::Exactly Solvable and Integrable Systems

A higher-order extension of the familiar Korteweg-de Vries equation is derived for internal solitary waves in a density- and current-stratified shear flow with a free surface. All coefficients of this extended Korteweg-de Vries equation are expressed in terms of integrals of the modal function for the linear long-wave theory. An illustrative example of a two-layer shear flow is considered, for which we discuss the parameter dependence of the coefficients in the extended Korteweg-de Vries equation.
  • References (23)
    23 references, page 1 of 3

    Benney, D. J.: Long nonlinear waves in fluid flows, J. Math. Phys., 45, 52-63, 1966.

    Benney, D. J., and Ko, D. R. S.: The propagation of long large amplitude internal waves, Stud. Appl. Math., 59, 187-199, 1978.

    Fokas, A. and Liu, Q. M.: Asymptotic integrability of water waves, Phys. Rev. Lett., 77, 2347-2351, 1996.

    Fokas, A., Grimshaw, R. H. J., and Pelinovsky, D. E.: On the asymptotic integrability of a higher-order evolution equation describing internal waves in a deep fluid, J. Math. Phys., 37, 3415- 3421, 1996.

    Funakoshi, M.: Long internal waves in a two-layer fluid, J. Phys. Soc. Japan, 54, 2470-2476, 1985.

    Funakoshi, M. and Oikawa, M.: Long internal waves of large amplitude in a two-layer fluid, J. Phys. Soc. Japan, 55, 128-144, 1986.

    Gear, J. A. and Grimshaw, R.: A second- order theory for solitary waves in shallow fluids, Phys. Fluids, 26, 14-29, 1983.

    Grimshaw, R.: Internal solitary waves, in: Advances in Coastal and Ocean Engineering, (Ed) Liu, P. L.-F., World Scientific Publishing Company, Singapore, 3, 1-30, 1997.

    Grimshaw, R., Pelinovsky, E. and Talipova, T.: The modified Korteweg-de Vries equation in the theory of the large amplitude internal waves, Non. Proc. Geophys., 4, 237-250, 1997.

    Holloway, P., Pelinovsky, E., Talipova, T., and Barnes, B.: A nonlinear model of internal tide transformation on the Australian NorthWest Shelf, J. Phys. Oceanography, 27, 871-896, 1997.

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