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Grimshaw , R.; Pelinovsky , E.; Poloukhina , O. (2002)
Publisher: European Geosciences Union (EGU)
Journal: Nonlinear Processes in Geophysics
Languages: English
Types: Article
Subjects: [ PHYS.ASTR.CO ] Physics [physics]/Astrophysics [astro-ph]/Cosmology and Extra-Galactic Astrophysics [astro-ph.CO], QC801-809, [ SDU.ASTR ] Sciences of the Universe [physics]/Astrophysics [astro-ph], Geophysics. Cosmic physics, Q, [ SDU.STU ] Sciences of the Universe [physics]/Earth Sciences, Science, Physics, QC1-999

Classified by OpenAIRE into

arxiv: Nonlinear Sciences::Exactly Solvable and Integrable Systems, Nonlinear Sciences::Pattern Formation and Solitons, Mathematics::Analysis of PDEs, Physics::Fluid Dynamics
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.
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    • 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.
    • Holloway, P., Pelinovsky, E. and, Talipova, T.: A generalised Korteweg-de Vries model of internal tide transformation in the coastal zone, J. Geophys. Res., 104, 18 333-18 350, 1999.
    • Kakutani, T. and Yamasaki, N.: Solitary waves in a two-layer fluid, J. Phys. Soc. Japan, 45, 674-679, 1978.
    • Kodama, Y.: Nearly integrable systems. Physica D, 16, 14-26, 1985.
    • Koop, C. G. and Butler, G.: An investigation of internal solitary waves in a two-fluid system, J. Fluid Mech., 112, 225-251, 1981.
    • Lamb, K. and Yan, L.: The evolution of internal wave undular bores: comparisons of a fully nonlinear numerical model with weakly nonlinear theory, J. Phys. Oceanography, 26, 2712-2734, 1996.
    • Lee, C. and Beardsley, R. C.: The generation of long nonlinear internal waves in a weakly stratified shear flow, J. Geophys. Res., 79, 453-462, 1974.
    • Long, R. R.: Solitary waves in one- and two-fluids systems, Tellus, 8, 460-471, 1956.
    • Marchant, T. R. and Smyth, N. F.: The extended Korteweg-de Vries equation and the resonant flow over topography, J. Fluid Mech., 221, 263-288, 1990.
    • Pelinovsky, E., Talipova, T., and Stepanyants, Yu.: Modelling of the propagation of nonlinear internal internal waves in horizontally inhomogeneous ocean, Izv. Atm. Oceanic Phys., 30, 79-85, 1994.
    • Pelinovsky, E. N., Poloukhina, O. E., and Lamb, K.: Nonlinear internal waves in the ocean stratified on density and current, Oceanology, 40, 805-815, 2000.
    • Prasad, D. and Akylas, T. R.: On the generation of shelves by long nonlinear waves in stratified flows, J. Fluid Mech., 346, 345-362, 1997.
    • Segur, H. and Hammack, J. L.: Soliton models of long internal waves, J. Fluid Mech., 118, 285-304, 1982.
    • Talipova, T., Pelinovsky, E., Lamb, K., Grimshaw, R., and Holloway, P.: Cubic effects at the intense internal wave propagation, Doklady Earth Sciences, 365, 241-244, 1999.
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