Journal of Applied Mathematics
Volume 2012 (2012), Article ID 491343, 17 pages
http://dx.doi.org/10.1155/2012/491343
Research Article

Forced ILW-Burgers Equation as a Model for Rossby Solitary Waves Generated by Topography in Finite Depth Fluids

Hongwei Yang,1,2,3,4 Baoshu Yin,1,4 Yunlong Shi,2 and Qingbiao Wang5

1Institute of Oceanology, China Academy of Sciences, Qingdao 266071, China
2Information School, Shandong University of Science and Technology, Qingdao 266590, China
3Graduate School, Chinese Academy of Sciences, Beijing 100049, China
4Key Laboratory of Ocean Circulation and Wave, Chinese Academy of Sciences, Qingdao 266071, China
5Department of Resource and Civil Engineering, Shandong University of Science and Technology, Taian 271019, China

Received 19 July 2012; Accepted 6 September 2012

Academic Editor: Turgut Öziş

Copyright © 2012 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.

Abstract

The paper presents an investigation of the generation, evolution of Rossby solitary waves generated by topography in finite depth fluids. The forced ILW- (Intermediate Long Waves-) Burgers equation as a model governing the amplitude of solitary waves is first derived and shown to reduce to the KdV- (Korteweg-de Vries-) Burgers equation in shallow fluids and BO- (Benjamin-Ono-) Burgers equation in deep fluids. By analysis and calculation, the perturbation solution and some conservation relations of the ILW-Burgers equation are obtained. Finally, with the help of pseudospectral method, the numerical solutions of the forced ILW-Burgers equation are given. The results demonstrate that the detuning parameter holds important implications for the generation of the solitary waves. By comparing with the solitary waves governed by ILW-Burgers equation and BO-Burgers equation, we can conclude that the solitary waves generated by topography in finite depth fluids are different from that in deep fluids.