中国物理B ›› 1994, Vol. 3 ›› Issue (12): 900-908.doi: 10.1088/1004-423X/3/12/004

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SOLITARY WAVES IN MARANGONI-BENARD CONVECTING FLUID

黄国翔   

  1. Department of Physics, East China Normal University, Shanghai 200062, China
  • 收稿日期:1994-01-03 出版日期:1994-12-20 发布日期:1994-12-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China and by the Natural Science Foundation of East China Normal University.

SOLITARY WAVES IN MARANGONI-BéNARD CONVECTING FLUID

HUANG GUO-XIANG (黄国翔)   

  1. Department of Physics, East China Normal University, Shanghai 200062, China
  • Received:1994-01-03 Online:1994-12-20 Published:1994-12-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China and by the Natural Science Foundation of East China Normal University.

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摘要： In this paper the evolution of nonlinear long surface waves in a Marangoni-Bénard convecting fluid is considered. The fluid system is bounded below by an isothermic plane and above a free deformable surface, on which a heat flux is fixed. We show that the nonlinear behavior of the long surface wave is governed by the Korteweg-de Vries equation when the Rayleigh number is near its critical value. A head-on collision between two solitary waves traveling from opposite directions is also investigated by use of the Poincaré-Lighthill-Kuo method. The results show that the solitary waves emerging from the collision can preserve their original identities to the second order. The phase shifts due to the collision are calculated analytically.

Abstract: In this paper the evolution of nonlinear long surface waves in a Marangoni-Bénard convecting fluid is considered. The fluid system is bounded below by an isothermic plane and above a free deformable surface, on which a heat flux is fixed. We show that the nonlinear behavior of the long surface wave is governed by the Korteweg-de Vries equation when the Rayleigh number is near its critical value. A head-on collision between two solitary waves traveling from opposite directions is also investigated by use of the Poincaré-Lighthill-Kuo method. The results show that the solitary waves emerging from the collision can preserve their original identities to the second order. The phase shifts due to the collision are calculated analytically.

中图分类号:  (Solitary waves)

  • 47.35.Fg
47.55.P- (Buoyancy-driven flows; convection) 47.20.-k (Flow instabilities)