- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Advances in Mechanical Engineering
Volume 2013 (2013), Article ID 289269, 10 pages
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.
- R. R. Long, “Solitary waves in the westerlies,” Journal of the Atmospheric Sciences, vol. 21, pp. 197–200, 1964.
- D. J. Benney, “Long non-linear waves in fluid ows,” Journal of Mathematical Physics, vol. 45, pp. 52–63, 1966.
- L. G. Rederopp, “On the theory of solitary Rossby waves,” Journal of Fluid Mechanics, vol. 82, pp. 725–745, 1977.
- H. Ono, “Algebraic Rossby wave soliton,” Journal of the Physical Society of Japan, vol. 50, no. 8, pp. 2757–2761, 1981.
- R. Grimshaw, “Slowly varying solitary waves in deep fluids,” Proceedings of the Royal Society A, vol. 376, pp. 319–332, 1981.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- D. H. Luo, “Algebraic solitary Rossby wave in the atmosphere,” Acta Meteorologica Sinica, vol. 49, pp. 269–277, 1991.
- 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.
- 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.
- 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.
- 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.
- 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.
- O. E. Polukhina and A. A. Kurkin, “Improved theory of nonlinear topographic Rossby waves,” Oceanology, vol. 45, no. 5, pp. 607–616, 2005.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- A. G. Davies and A. D. Heathershaw, “Surface-wave propagation over sinusoidally varying topography,” Journal of Fluid Mechanics, vol. 144, pp. 419–443, 1984.
- 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.
- P. Hall, “Alternating bar instabilities in unsteady channel flows over erodible beds,” Journal of Fluid Mechanics, no. 499, pp. 49–73, 2004.
- 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.
- 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.
- B. Wang and H. Y. Weng, Introduction of Geophysical Fluid Dynamics, Ocean Press, Beijing, China, 1981.
- S. K. Liu and S. D. Liu, Atmospheric Dynamics, Beijing University Press, Beijing, China, 1991.
- 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.
- 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.
- 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.
- H. Ono, “Algebraic solitary waves in stratified fluids,” Journal of the Physical Society of Japan, vol. 39, no. 4, pp. 1082–1091, 1975.
- B. Fornberg, A Practical Guide to Pseudo-Spectral Method, Cambridge University Press, Cambridge, UK, 1996.