Free Access
Issue
Math. Model. Nat. Phenom.
Volume 7, Number 2, 2012
Solitary waves
Page(s) 52 - 65
DOI https://doi.org/10.1051/mmnp/20127205
Published online 29 February 2012
  1. H. Cho, T. Shepherd, V. Vladimirov. Application of the direct Liapunov method to the problem of symmetric stability in the atmosphere. J. Atmosph. Sci., (1993), 50 (6), 822-836. [CrossRef] [Google Scholar]
  2. W. Craig, P. Guyenne, H. Kalisch. Hamiltonian long-wave expansions for the free surfaces and interfaces. Comm. Pure Appl. Math., (2005), 58, 1587-1641. [CrossRef] [MathSciNet] [Google Scholar]
  3. E. Dewan, R. Picard, R. O’Neil, H. Gardiner, J. Gibson. MSX satellite observations of thunderstorm-generated gravity waves in mid-wave infrared images of the upper stratosphere. Geophys. Res. Lett., (1998), 25, 939-942. [CrossRef] [Google Scholar]
  4. S. Dalziel, G. Hughes, B. Sutherland. Whole field density measurements by synthetic schlieren. Experiments in Fluids, (2000), 28, 322-337. [CrossRef] [Google Scholar]
  5. T. Dauxois, W. Young. Near-critical reflection of internal waves. J. Fluid Mech., (1999), 390, 271-295. [CrossRef] [MathSciNet] [Google Scholar]
  6. R. Fjortoft. R, Application of integral theorems in deriving criteria of stability for laminar flows and for the baroclinic circular vortex. Geophys. Publ., (1950), 17(6), 1-52. [Google Scholar]
  7. M. Flynn, K. Onu, B. Sutherland. Internal wave excitation by a vertically oscillating sphere. J. Fluid Mech., (2003), 494, 65-93. [CrossRef] [MathSciNet] [Google Scholar]
  8. C. Garrett. Internal tides and ocean mixing. Science, (2003), 301 (5641), 1858-1859, doi :10.1126/science.1090002. [Google Scholar]
  9. C. Garrett, W. Munk. Space time scale of internal waves. A progress report. J. Geophys. Res., (1975), 80, 291-297. [CrossRef] [Google Scholar]
  10. A. Gill. Atmosphere-Ocean Dynamics. New York, etc., Academic Press, (1983). [Google Scholar]
  11. J. Hadamard. Lectures on Cauchy’s problem in linear partial differential equations. Yale University Press, New Haven, (1983). [Google Scholar]
  12. J. Hadamard. The problem of diffusion of waves. Annals of Mathematics, Ser. 2 43 : 510-522, (1942). [Google Scholar]
  13. N. Ibragimov. Elementary Lie group analysis of ordinary differential equations. John Wiley & Sons, Chichester, (1999). [Google Scholar]
  14. N. Ibragimov. Transformation Groups Applied to Mathematical Physics. Nauka, Moscow (1983), English. transl., Reidel, Dordrecht. [Google Scholar]
  15. N. Ibragimov Ed. CRC Handbook of Lie group analysis of differential equations (CRC Press, Boca Raton) ; Vol. 1 (1994, 429 p), Vol. 2 (1995, 546 p.), Vol. 3 (1996, 536 p.). [Google Scholar]
  16. N. Ibragimov. A new conservation theorem J. Math. Anal. Appl., (2007), 333 : 311-328. [CrossRef] [Google Scholar]
  17. N. Ibragimov. Group analysis - a microscope of mathematical modelling. I : Galilean relativity in diffusion models. Selected works (ALGA Publications, Karlskrona), (2006), 2 : 225-243. [Google Scholar]
  18. N. Ibragimov. Conformal invariance and Huygens’ principle. Soviet Mathematics Doklady, (1970), 11(5) : 1153-1157. [Google Scholar]
  19. N. Ibragimov. Application of group analysis to liquid metal systems. Archives of ALGA, (2010), 6 : 91-101. [Google Scholar]
  20. N. Ibragimov. Lie group analysis of Moffatt’s model in metallurgical industry. Nonlinear Math. Phys., (2011), 18, 143-162. [CrossRef] [MathSciNet] [Google Scholar]
  21. N. Ibragimov, R. Ibragimov, V. Kovalev. Group analysis of nonlinear internal waves in oceans. Archives of ALGA, (2009), 6, 45-54. [Google Scholar]
  22. N. Ibragimov, R. Ibragimov. Applications of Lie Group Analysis in Geophysical Fluid Dynamics. Series on Complexity, Nonlinearity and Chaos, (2011), Vol 2, World Scientific Publishers, ISBN : 978-981-4340-46-5. [Google Scholar]
  23. N. Ibragimov, R. Ibragimov. Internal gravity wave beams as invariant solutions of Boussinesq equations in geophysical fluid dynamics. Comm. Nonlinear Sci. Num. Simulat., (2010), 15, 1989-2002. [CrossRef] [Google Scholar]
  24. R. Ibragimov. Oscillatory nature and dissipation of the internal wave energy spectrum in the deep ocean. Eur. Phys. J. Appl. Phys., (2007), 40, 315-334. [CrossRef] [EDP Sciences] [Google Scholar]
  25. R. Ibragimov. Generation of internal tides by an oscillating background flow along a corrugated slope. Phys. Scr., (2008), 78, 065801. [CrossRef] [Google Scholar]
  26. R. Ibragimov, D. Pelinovsky. Incompressible viscous fluid flows in a thin spherical shell. J. Math. Fluid. Mech., (2009), 11, 60-90. [CrossRef] [MathSciNet] [Google Scholar]
  27. R. Ibragimov, N. Ibragimov. Effects of rotation on self-resonant internal gravity waves. Ocean Modelling, (2010), 31, 80-87. [CrossRef] [Google Scholar]
  28. R. Ibragimov, M. Dameron. Spinning phenomena and energetics of spherically pulsating patterns in stratified fluids. Phys. Scr., (2011), 84, 015402. [CrossRef] [Google Scholar]
  29. A. Javam, J. Imberger, S. Armfield. Numerical study of internal wave-wave interactions in a stratified fluid. J. Fluid Mech., (2000), 415, 65-87. [CrossRef] [MathSciNet] [Google Scholar]
  30. H. Kalisch, N. Nguyen. On the stability of internal waves. J. Phys. A, (2010), 43, 495205. [CrossRef] [MathSciNet] [Google Scholar]
  31. H. Kalisch, J. Bona. Modes for internal waves in deep water. Disc. Cont. Dyn. Sys. (2000), 6, 1-19. [CrossRef] [Google Scholar]
  32. A. Kistovich, Y. Chashechkin. Nonlinear interactions of two dimensional packets of monochromatic internal waves. Izv. Atmos. Ocean. Phys., (1991), 27 (12) 946-951. [Google Scholar]
  33. F. Lam, L. Mass, T. Gerkema. Spatial structure of tidal and residual currents as observed over the shelf break in the Bay of Biscay. Deep-See Res., (2004), I 51, 10751096. [Google Scholar]
  34. P. Lombard, J. Riley. On the breakdown into turbulence of propagating internal waves. Dyn. Atmos. Oceans, (1996), 23, 345-355. [CrossRef] [Google Scholar]
  35. H. Moffatt. High frequency excitation of liquid metal systems. Metallurgical Applications of Magnetohydrodynamics, (1984), (Metals Society, London) 180-189. [Google Scholar]
  36. P. Müller, G. Holloway, F. Henyey, N. Pomphrey. Nonlinear interactions among internal gravity waves. Rev. Geophys., (1986), 24, 3, 493-536. [NASA ADS] [CrossRef] [Google Scholar]
  37. J. Nash, E. Kunze, C. Lee, T. Sanford. Structure of the baroclinic tide generated at Keana Ridge, Hawaii. J. Phys. Oceanogr., (2006), 36, 1123-1135. [CrossRef] [Google Scholar]
  38. P. Olver. Applications of Lie groups to differential equations. Springer-Verlag, New York, 2nd ed. 1993. [Google Scholar]
  39. L. Ovsyannikov. Group Analysis of Differential Equations. Nauka, Moscow, (1978), English transl., ed. W.F. Ames, Academic Press, New York (1982). [Google Scholar]
  40. D. Ramsden, G. Holloway. Energy transfers across an internal wave-vortical mode spectrum. J. Geophys. Res., (1992), 97, 3659-3668. [CrossRef] [Google Scholar]
  41. J. Riley, R. Metcalfe, M. Weissman. Direct numerical simulations of homogeneous turbulence in density-stratified fluids. Nonlinear properties of internal waves, (1981), 76, edited by B.J. West, pp. 79-112, Americal Institute of Physics, New York. [Google Scholar]
  42. T. Shepherd. Symmetries, conservation laws, and Hamiltonian structure in geophysical fluid dynamics. Advances in Geophysics, (1990), 32, 287-338 [CrossRef] [Google Scholar]
  43. C. Staquet, J. Sommeria. Internal Gravity Waves : From instabilities to turbulence. Annu. Rev. Fluid Mech., (2002), 34, 559-593. [NASA ADS] [CrossRef] [Google Scholar]
  44. A. Tabaei, T. Akylas, K. Lamb. Nonlinear effects in reflecting and colliding internal wave beams. J. Fluid Mech., (2005), 526, 217-243. [CrossRef] [MathSciNet] [Google Scholar]
  45. A. Tabaei, T. Akylas. Nonlinear internal gravity wave beams. J. Fluid Mech., (2003), 482, 141-161. [CrossRef] [MathSciNet] [Google Scholar]
  46. S. Teoh, J. Imberger, G. Ivey. Laboratory study of the interactions between two internal wave rays. J. Fluid Mech., (1997), 336:91. [CrossRef] [Google Scholar]
  47. K. Winters, E. D’Asaro. Direct simulation of internal wave energy transfer. J. Phys. Oceanogr., (1997), 9, 235-243. [Google Scholar]
  48. C. Wunsch, R. Ferrari. Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech., (2004), 36, 281-314. [CrossRef] [Google Scholar]
  49. H. Zhang, B. King, H. Swinney. Resonant generation of internal waves on a model continental slope. Phys. Rev. Let., (2008), 100, 244504. [CrossRef] [Google Scholar]

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