Free Access
Math. Model. Nat. Phenom.
Volume 9, Number 5, 2014
Spectral problems
Page(s) 73 - 82
Published online 17 July 2014
  1. J. Adcroft et al. MITgcm User Manual. MIT Department of EAPS, Cambridge, MA, 2008. [Google Scholar]
  2. L.F. Bartholomeusz. The reflection of long waves at a step. Proc. Camb. Philos. Soc., 54 (1958), 106–118. [CrossRef] [Google Scholar]
  3. G.P. Germain. Coefficients de réflexion et de transmission en eau peu profonde. Instytut Budownictwa Wodnego, Gdansk, Rozprawy Hydrotechniczne, Rep. no. 46, 5–13 (in French). [Google Scholar]
  4. K.A. Gorshkov, L.A. Ostrovsky, V.V. Papko, E.N. Pelinovsky. Electromodeling of finite amplitude water waves. Bull. Roy. Soc. New Zealand, 15 (1976), 123–131. [Google Scholar]
  5. R. Grimshaw, E. Pelinovsky, T. Talipova. Fission of a weakly nonlinear interfacial solitary wave at a step. Geophys. Astrophys. Fluid Dyn., 102 (2008), no. 2, 179–194. [CrossRef] [MathSciNet] [Google Scholar]
  6. H. Lamb. Hydrodynamics. 6-th ed., Cambridge Univ. Press, Cambridge, 1932. [Google Scholar]
  7. M.A. Losada, C. Vidal, R. Medina. Experimental study of the evolution of a solitary wave at the abrupt junction. J. Geophys. Res., 94 (1989), no. C10, 14, 557–14, 566. [CrossRef] [Google Scholar]
  8. V. Maderich, T. Talipova, R. Grimshaw, E. Pelinovsky, B. H. Choi, I. Brovchenko, K. Terletska, D.C. Kim. The transformation of an interfacial solitary wave of elevation at a bottom step. Nonlin. Processes Geophys., 16 (2009), 33–42. [CrossRef] [Google Scholar]
  9. V. Maderich, T. Talipova, R. Grimshaw, K. Terletska, I. Brovchenko, E. Pelinovsky, B.H. Choi. Interaction of a large amplitude interfacial solitary wave of depression with a bottom step. Phys. Fluids, 22 (2010), 076602. [CrossRef] [Google Scholar]
  10. V.A. Makarov, A.B. Menzin. Electrical Analog modeling in Oceanology, Leningrad, Gidrometeoizdat, 1976 (in Russian). [Google Scholar]
  11. J. Marshal, C. Hill, L. Perelman, A. Adcroft. Hydrostatic, quasi-hydrostatic, and nonhydrostatic ocean modeling. J. Geophys. Res., 102 no. C3, (1997), 5,733–5,752. [Google Scholar]
  12. J. Marshal, A. Adcroft, C. Hill, L. Perelman, C. Heisey. A finite-volume, incompressible Navier–Stokes model for studies of the ocean on parallel computers. J. Geophys. Res., 102 (1997), no. C3, 5,753–5,766. [CrossRef] [Google Scholar]
  13. J.S. Marshal, P.M. Naghdi. Wave reflection and transmission by steps and rectangular obstacles in channels of finite depth. Theoret. Comput. Fluid Dynamics, 1 (1990), 287–301. [CrossRef] [Google Scholar]
  14. S.R. Massel. Harmonic generation by waves propagating over a submerged step. Coastal Eng., 7 (1983), 357–380. [CrossRef] [Google Scholar]
  15. S.R. Massel. Hydrodynamics of the coastal zone, Elsevier, Amsterdam, 1989. [Google Scholar]
  16. J.W. Miles. Surface-wave scattering matrix for a shelf. J. Fluid Mech., 28 (1967), pt. 4, 755–767. [CrossRef] [Google Scholar]
  17. N. Mirchina, E. Pelinovsky. Nonlinear transformation of long waves at a bottom step. J. Korean Soc. Coastal Ocean Eng., 4 (1992), no. 3, 161–167. [Google Scholar]
  18. J.N. Newman. Propagation of water waves over an infinite step. J. Fluid Mech. 23 (1965), pt. 2, 339–415. [Google Scholar]
  19. E.N. Pelinovsky. On the solitary wave transformation on a shelf with the horizontal bottom. In: Theoretical and Experimental Studies of Tsunami, Eds. S.L. Solov’yov, A.I. Ivashchenko, and V.M. Kaistrenko, Moscow, Nauka, (1977), 61–63 (in Russian). [Google Scholar]
  20. E.N. Pelinovsky. Hydrodynamics of Tsunami Waves, Nizhny Novogrod, IAP RAS, 1996 (in Russian). [Google Scholar]
  21. E. Pelinovsky, B.H. Choi, T. Talipova, S.B. Wood, D.Ch. Kim. Solitary wave transformation on the underwater step: Asymptotic theory and numerical experiments. Appl. Math. and Comp., 217 (2010), no. 1, 704–1,718. [CrossRef] [Google Scholar]
  22. F.J. Seabra-Santos, D.P. Renouard, A.M. Temperville. Numerical and experimental study of the transformation of a solitary wave over a shelf or isolated obstacle. J. Fluid Mech., 176 (1987), 17–134. [Google Scholar]
  23. L.N. Sretensky. The Theory of Wave Motions of a Liquid, Moscow, Nauka, 1977 (in Russian). [Google Scholar]
  24. Y.A. Stepanyants. On soliton propagation in the inhomogeneous long line. Radiotekhnika i Elektronika, 22, (1977), no. 5, 995–1,002 (in Russian). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.