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Advances in Mechanical Engineering
Volume 2013 (2013), Article ID 289269, 10 pages
http://dx.doi.org/10.1155/2013/289269
Research Article

Rossby Solitary Waves Generated by Wavy Bottom in Stratified Fluids

1College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao, Shandong 266590, China
2Institute of Oceanology, China Academy of Sciences, Qingdao, Shandong 266071, China
3Key Laboratory of Ocean Circulation and Wave, Chinese Academy of Sciences, Qingdao, Shandong 266071, China
4Faculty of Science, Beijing Jiaotong University, Beijing 100044, China

Received 5 October 2012; Revised 10 December 2012; Accepted 24 December 2012

Academic Editor: Oronzio Manca

Copyright © 2013 Hongwei Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. R. Long, “Solitary waves in the westerlies,” Journal of the Atmospheric Sciences, vol. 21, pp. 197–200, 1964.
  2. D. J. Benney, “Long non-linear waves in fluid ows,” Journal of Mathematical Physics, vol. 45, pp. 52–63, 1966.
  3. L. G. Rederopp, “On the theory of solitary Rossby waves,” Journal of Fluid Mechanics, vol. 82, pp. 725–745, 1977.
  4. H. Ono, “Algebraic Rossby wave soliton,” Journal of the Physical Society of Japan, vol. 50, no. 8, pp. 2757–2761, 1981. View at Scopus
  5. R. Grimshaw, “Slowly varying solitary waves in deep fluids,” Proceedings of the Royal Society A, vol. 376, pp. 319–332, 1981.
  6. L. Dehai and J. Liren, “Algebraic rossby solitary wave and blocking in the atmosphere,” Advances in Atmospheric Sciences, vol. 5, no. 4, pp. 445–454, 1988. View at Publisher · View at Google Scholar · View at Scopus
  7. L. Shi-kuo and T. Ben-kui, “Rossby waves with the change of β,” Applied Mathematics and Mechanics, vol. 13, no. 1, pp. 39–49, 1992. View at Publisher · View at Google Scholar · View at Scopus
  8. L. G. Yang, Y. J. Hou, Q. Xie, and M. H. Cheng, “Nonlinear Rossby wave in geophysical fluid,” Acta Oceanologica Sinica, vol. 20, pp. 133–138, 1998.
  9. S. Jian and Y. Lian-Gui, “Modified KdV equation for solitary rossby waves with β effect in barotropic fluids,” Chinese Physics B, vol. 18, no. 7, pp. 2873–2877, 2009. View at Publisher · View at Google Scholar · View at Scopus
  10. H. W. Yang, B. S. Yin, H. H. Dong, and Z. D. Ma, “Generation of solitary Rossby waves by unstable topography,” Communications in Theoretical Physics, vol. 57, pp. 473–476, 2012.
  11. Z. H. Xu, B. S. Yin, and Y. J. Hou, “Response of internal solitary waves to tropical storm Washi in the northwestern South China Sea,” Annales Geophysicae, vol. 29, no. 11, pp. 2181–2187, 2011.
  12. T. Kubota, D. R. S. Ko, and L. D. Dobbs, “Weakly-nonlinear, long internal gravity waves in stratified fluids of finite depth,” Journal of Hydrology, vol. 12, no. 4, pp. 157–165, 1978. View at Scopus
  13. D. H. Luo, “Algebraic solitary Rossby wave in the atmosphere,” Acta Meteorologica Sinica, vol. 49, pp. 269–277, 1991.
  14. W. X. Ma and Y. You, “Solving the Korteweg-de Vries equation by its bilinear form: wronskian solutions,” Transactions of the American Mathematical Society, vol. 357, no. 5, pp. 1753–1778, 2005. View at Publisher · View at Google Scholar · View at Scopus
  15. Z. J. Qiao and T. X. Xu, “Darboux transformation and shock solitons for complex MKdV equation,” Pacific Journal of Applied Mathematics, vol. 3, pp. 1–10, 2010.
  16. Z. Qiao and J. Li, “Negative-order KdV equation with both solitons and kink wave solutions,” Europhysics Letters, vol. 94, no. 5, Article ID 50003, 2011. View at Publisher · View at Google Scholar · View at Scopus
  17. X. H. Liu, W. G. Zhang, and Z. M. Li, “Application of improved (G'/G)-expansion method to traveling wave solutions of two nonlinear evolution equations,” The Advances in Applied Mathematics and Mechanics, vol. 4, pp. 122–130, 2012.
  18. G. Gottwald and R. Grimshaw, “The effect of topography on the dynamics of interacting solitary waves in the context of atmospheric blocking,” Journal of the Atmospheric Sciences, vol. 56, no. 21, pp. 3663–3678, 1999. View at Scopus
  19. O. E. Polukhina and A. A. Kurkin, “Improved theory of nonlinear topographic Rossby waves,” Oceanology, vol. 45, no. 5, pp. 607–616, 2005. View at Scopus
  20. L. Yang, C. Da, J. Song, H. Zhang, H. Yang, and Y. Hou, “Rossby waves with linear topography in barotropic fluids,” Chinese Journal of Oceanology and Limnology, vol. 26, no. 3, pp. 334–338, 2008. View at Publisher · View at Google Scholar · View at Scopus
  21. J. Song and L. G. Yang, “Modified KdV equations for solitary Rossby waves with nonlinear topography in barotropic fluids,” Progress in Geophysics, vol. 25, pp. 543–547, 2010.
  22. H. W. Yang, B. S. Yin, and Y. L. Shi, “Forced dissipative Boussinesq equation for solitary waves excited by unstable topography,” Nonlinear Dynamics, vol. 70, no. 2, pp. 1389–1396, 2012. View at Publisher · View at Google Scholar
  23. H. N. Cui, X. Q. Yang, X. F. Pang, and L. W. Xiang, “A study on the behavior of non-propagating solitary wave,” Journal of Hydrodynamics, Series B, vol. 6, pp. 18–25, 1991.
  24. G. D. Zhou, Q. T. Liu, G. X. Wang, and D. M. Pang, “Non-uniformity coefficient effects in alluvial streams,” Journal of Hydrodynamics, Series A, vol. 18, pp. 576–583, 2003.
  25. X. Li, Y. G. Wang, and S. M. Sha, “Numerical simulation of topography change in reclaimed land along coast of South China Sea,” Journal of Hydrodynamics, vol. 14, no. 1, pp. 87–92, 2002. View at Scopus
  26. A. G. Davies and A. D. Heathershaw, “Surface-wave propagation over sinusoidally varying topography,” Journal of Fluid Mechanics, vol. 144, pp. 419–443, 1984. View at Scopus
  27. A. G. Davies and C. Villaret, “Prediction of sand transport rates by waves and currents in the coastal zone,” Continental Shelf Research, vol. 22, no. 18-19, pp. 2725–2737, 2002. View at Publisher · View at Google Scholar · View at Scopus
  28. P. Hall, “Alternating bar instabilities in unsteady channel flows over erodible beds,” Journal of Fluid Mechanics, no. 499, pp. 49–73, 2004. View at Publisher · View at Google Scholar · View at Scopus
  29. Z. R. Wu, Y. L. Cheng, and S. L. Wang, “Numerical study on effect of waving bed on the surface wave,” Journal of Hydrodynamics, vol. 18, no. 4, pp. 464–468, 2006. View at Publisher · View at Google Scholar · View at Scopus
  30. S. Kalliadasis and G. M. Homsy, “Stability of free-surface thin-film flows over topography,” Journal of Fluid Mechanics, vol. 448, pp. 387–410, 2001. View at Scopus
  31. B. Wang and H. Y. Weng, Introduction of Geophysical Fluid Dynamics, Ocean Press, Beijing, China, 1981.
  32. S. K. Liu and S. D. Liu, Atmospheric Dynamics, Beijing University Press, Beijing, China, 1991.
  33. T. Warn and B. Brasnett, “The amplification and capture of atmospheric solitons by topography: a theory of the onset of regional blocking,” Journal of the Atmospheric Sciences, vol. 40, no. 1, pp. 28–38, 1983. View at Scopus
  34. K. L. Lv and H. S. Jiang, “Localized thermal forcing and formation of large amplitude quasi-steady disturbances,” Acta Meteorologica Sinica, vol. 56, pp. 424–435, 1998.
  35. L. Meng and K. L. Lv, “Dissipation and algebraic solitary long-waves excited by localized topography,” Chinese Journal of Computational Physics, vol. 19, pp. 159–167, 2002.
  36. H. Ono, “Algebraic solitary waves in stratified fluids,” Journal of the Physical Society of Japan, vol. 39, no. 4, pp. 1082–1091, 1975. View at Scopus
  37. B. Fornberg, A Practical Guide to Pseudo-Spectral Method, Cambridge University Press, Cambridge, UK, 1996.