中国物理B ›› 2015, Vol. 24 ›› Issue (9): 90205-090205.doi: 10.1088/1674-1056/24/9/090205

• GENERAL • 上一篇    下一篇

A new model for algebraic Rossby solitary waves in rotation fluid and its solution

陈耀登a b, 杨红卫c, 高玉芳a b, 尹宝树d e, 冯兴如d e   

  1. a Key Laboratory of Meteorological Disaster of Ministry of Education, Nanjing University of Information Science & Technology, Nanjing 210044, China;
    b Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University ofInformation Science & Technology, Nanjing 210044, China;
    c College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;
    d Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China;
    e Key Laboratory of Ocean Circulation and Wave, Chinese Academy of Sciences, Qingdao 266071, China
  • 收稿日期:2015-02-04 修回日期:2015-03-26 出版日期:2015-09-05 发布日期:2015-09-05
  • 基金资助:
    Project supported by the Shandong Provincial Key Laboratory of Marine Ecology and Environment and Disaster Prevention and Mitigation Project, China (Grant No. 2012010), the National Natural Science Foundation of China (Grant Nos. 41205082 and 41476019), the Special Funds for Theoretical Physics of the National Natural Science Foundation of China (Grant No. 11447205), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), China.

A new model for algebraic Rossby solitary waves in rotation fluid and its solution

Chen Yao-Deng (陈耀登)a b, Yang Hong-Wei (杨红卫)c, Gao Yu-Fang (高玉芳)a b, Yin Bao-Shu (尹宝树)d e, Feng Xing-Ru (冯兴如)d e   

  1. a Key Laboratory of Meteorological Disaster of Ministry of Education, Nanjing University of Information Science & Technology, Nanjing 210044, China;
    b Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University ofInformation Science & Technology, Nanjing 210044, China;
    c College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;
    d Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China;
    e Key Laboratory of Ocean Circulation and Wave, Chinese Academy of Sciences, Qingdao 266071, China
  • Received:2015-02-04 Revised:2015-03-26 Online:2015-09-05 Published:2015-09-05
  • Contact: Yang Hong-Wei E-mail:hwyang1979@163.com
  • Supported by:
    Project supported by the Shandong Provincial Key Laboratory of Marine Ecology and Environment and Disaster Prevention and Mitigation Project, China (Grant No. 2012010), the National Natural Science Foundation of China (Grant Nos. 41205082 and 41476019), the Special Funds for Theoretical Physics of the National Natural Science Foundation of China (Grant No. 11447205), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), China.

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摘要： A generalized Boussinesq equation that includes the dissipation effect is derived to describe a kind of algebraic Rossby solitary waves in a rotating fluid by employing perturbation expansions and stretching transformations of time and space. Using this equation, the conservation laws of algebraic Rossby solitary waves are discussed. It is found that the mass, the momentum, the energy, and the velocity of center of gravity of the algebraic solitary waves are conserved in the propagation process. Finally, the analytical solution of the equation is generated. Based on the analytical solution, the properties of the algebraic solitary waves and the dissipation effect are discussed. The results point out that, similar to classic solitary waves, the dissipation can cause the amplitude and the speed of solitary waves to decrease; however, unlike classic solitary waves, the algebraic solitary waves can split during propagation and the decrease of the detuning parameter can accelerate the occurrence of the solitary waves fission phenomenon.

关键词: generalized Boussinesq equation, algebraic Rossby solitary waves, dissipation effect, solitary waves fission

Abstract: A generalized Boussinesq equation that includes the dissipation effect is derived to describe a kind of algebraic Rossby solitary waves in a rotating fluid by employing perturbation expansions and stretching transformations of time and space. Using this equation, the conservation laws of algebraic Rossby solitary waves are discussed. It is found that the mass, the momentum, the energy, and the velocity of center of gravity of the algebraic solitary waves are conserved in the propagation process. Finally, the analytical solution of the equation is generated. Based on the analytical solution, the properties of the algebraic solitary waves and the dissipation effect are discussed. The results point out that, similar to classic solitary waves, the dissipation can cause the amplitude and the speed of solitary waves to decrease; however, unlike classic solitary waves, the algebraic solitary waves can split during propagation and the decrease of the detuning parameter can accelerate the occurrence of the solitary waves fission phenomenon.

Key words: generalized Boussinesq equation, algebraic Rossby solitary waves, dissipation effect, solitary waves fission

中图分类号:  (Partial differential equations)

  • 02.30.Jr
47.35.Fg (Solitary waves) 92.10.Hm (Ocean waves and oscillations)