Abstract and Applied Analysis
Volume 2014, Article ID 175841, 5 pages
http://dx.doi.org/10.1155/2014/175841
Benjamin-Ono-Burgers-MKdV Equation for Algebraic Rossby Solitary Waves in Stratified Fluids and Conservation Laws
1College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, China
2The First Institute of Oceanography, SOA, Qingdao 266061, China
3Institute of Oceanology, China Academy of Sciences, Qingdao 266071, China
4Key Laboratory of Ocean Circulation and Wave, Chinese Academy of Sciences, Qingdao 266071, China
Received 2 July 2014; Revised 25 August 2014; Accepted 26 August 2014; Published 16 October 2014
Academic Editor: Yufeng Zhang
Copyright © 2014 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
In the paper, by using multiple-scale method, the Benjamin-Ono-Burgers-MKdV (BO-B-MKdV) equation is obtained which governs algebraic Rossby solitary waves in stratified fluids. This equation is first derived for Rossby waves. By analysis and calculation, some conservation laws are derived from the BO-B-MKdV equation without dissipation. The results show that the mass, momentum, energy, and velocity of the center of gravity of algebraic Rossby waves are conserved and the presence of a small dissipation destroys these conservations.