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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.

Abstract

Rossby solitary waves generated by a wavy bottom are studied in stratified fluids. From the quasigeostrophic vorticity equation including a wavy bottom and dissipation, by employing perturbation expansions and stretching transforms of time and space, a forced KdV-ILW-Burgers equation is derived through a new scale analysis, modelling the evolution of Rossby solitary waves. By analysis and calculation, based on the conservation relations of the KdV-ILW-Burgers equation, the conservation laws of Rossby solitary waves are obtained. Finally, the numerical solutions of the forced KdV-ILW-Burgers equation are given by using the pseudospectral method, and the evolutional feature of solitary waves generated by a wavy bottom is discussed. The results show that, besides the solitary waves, an additional harmonic wave appears in the wavy bottom forcing region, and they propagate independently and do not interfere with each other. Furthermore, the wavy bottom forcing can prevent wave breaking to some extent. Meanwhile, the effect of dissipation and detuning parameter on Rossby solitary waves is also studied. Research on the wavy bottom effect on the Rossby solitary waves dynamics is of interest in analytical geophysical fluid dynamics.