中国物理B ›› 2009, Vol. 18 ›› Issue (10): 4074-4082.doi: 10.1088/1674-1056/18/10/003

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Application of higher-order KdV--mKdV model with higher-degree nonlinear terms to gravity waves in atmosphere

李子良   

  1. Department of Marine Meteorology, Laboratory of Air-Sea Interaction and Climate, Ocean University of China, Qingdao 266100, China
  • 收稿日期:2009-01-31 修回日期:2009-05-14 出版日期:2009-10-20 发布日期:2009-10-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 40775069).

Application of higher-order KdV--mKdV model with higher-degree nonlinear terms to gravity waves in atmosphere

Li Zi-Liang(李子良)†   

  1. Department of Marine Meteorology, Laboratory of Air-Sea Interaction and Climate, Ocean University of China, Qingdao 266100, China
  • Received:2009-01-31 Revised:2009-05-14 Online:2009-10-20 Published:2009-10-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 40775069).

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摘要： Higher-order Korteweg-de Vries (KdV)-modified KdV (mKdV) equations with a higher-degree of nonlinear terms are derived from a simple incompressible non-hydrostatic Boussinesq equation set in atmosphere and are used to investigate gravity waves in atmosphere. By taking advantage of the auxiliary nonlinear ordinary differential equation, periodic wave and solitary wave solutions of the fifth-order KdV--mKdV models with higher-degree nonlinear terms are obtained under some constraint conditions. The analysis shows that the propagation and the periodic structures of gravity waves depend on the properties of the slope of line of constant phase and atmospheric stability. The Jacobi elliptic function wave and solitary wave solutions with slowly varying amplitude are transformed into triangular waves with the abruptly varying amplitude and breaking gravity waves under the effect of atmospheric instability.

Abstract: Higher-order Korteweg-de Vries (KdV)-modified KdV (mKdV) equations with a higher-degree of nonlinear terms are derived from a simple incompressible non-hydrostatic Boussinesq equation set in atmosphere and are used to investigate gravity waves in atmosphere. By taking advantage of the auxiliary nonlinear ordinary differential equation, periodic wave and solitary wave solutions of the fifth-order KdV--mKdV models with higher-degree nonlinear terms are obtained under some constraint conditions. The analysis shows that the propagation and the periodic structures of gravity waves depend on the properties of the slope of line of constant phase and atmospheric stability. The Jacobi elliptic function wave and solitary wave solutions with slowly varying amplitude are transformed into triangular waves with the abruptly varying amplitude and breaking gravity waves under the effect of atmospheric instability.

Key words: gravity waves, higher-order KdV--mKdV equation, propagating, breaking

中图分类号:  (Acoustic gravity waves, tides, and compressional waves)

  • 92.60.hh