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Applied Mathematics and Mechanics (English Edition) ›› 2001, Vol. 22 ›› Issue (6): 730-740.

• 论文 • 上一篇    

ON THE RESONANT GENERATION OF WEAKLY NONLINEAR STOKES WAVES IN REGIONS WITH FAST VARYING TOPOGRAPHY AND FREE SURFACE CURRENT

黄虎1,2, 周锡1   

  1. 1. School of Civil Engineering, Tianjin University, Tianjin 300072, P.R.China;
    2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P.R.China
  • 收稿日期:1999-09-13 修回日期:2001-01-15 出版日期:2001-06-18 发布日期:2001-06-18
  • 通讯作者: HUI Chang-nian
  • 基金资助:
    the Doctoral Program Fund of China Education Commission (940562);the China National Foundation of High Performance Computer (96103)

ON THE RESONANT GENERATION OF WEAKLY NONLINEAR STOKES WAVES IN REGIONS WITH FAST VARYING TOPOGRAPHY AND FREE SURFACE CURRENT

HUANG Hu1,2, ZHOU Xi-reng 1   

  1. 1. School of Civil Engineering, Tianjin University, Tianjin 300072, P.R.China;
    2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P.R.China
  • Received:1999-09-13 Revised:2001-01-15 Online:2001-06-18 Published:2001-06-18
  • Supported by:
    the Doctoral Program Fund of China Education Commission (940562);the China National Foundation of High Performance Computer (96103)

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摘要： The effect of nonlinearity on the free surface wave resonated by an incident flow over rippled beds, which consist of fast varying topography superimposed on an otherwise slowly varying mean depth, is studied using a WKBJ-type perturbation approach. Synchronous, superharmonic and in particular subharmonic resonance were selectively excited over the fast varying topography with corresponding wavelengths. For a steady current the dynamical system is autonomous and the possible nonlinear steady states and their stability were investigated. When the current has a small oscillatory component the dynamical system becomes non-autonomous, chaos is now possible.

Abstract: The effect of nonlinearity on the free surface wave resonated by an incident flow over rippled beds, which consist of fast varying topography superimposed on an otherwise slowly varying mean depth, is studied using a WKBJ-type perturbation approach. Synchronous, superharmonic and in particular subharmonic resonance were selectively excited over the fast varying topography with corresponding wavelengths. For a steady current the dynamical system is autonomous and the possible nonlinear steady states and their stability were investigated. When the current has a small oscillatory component the dynamical system becomes non-autonomous, chaos is now possible.

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