On the Resonant Generation of Weakly Nonlinear Stokes Waves in Regions with Fast Varying Topography and Free Surface Current |
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| Authors: | Hu Huang Xi-reng Zhou |
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| Institution: | 1. School of Civil Engineering, Tianjin University, Tianjin 300072, P R China;Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P R China
2. School of Civil Engineering, Tianjin University, Tianjin 300072, P R China |
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| 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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| Keywords: | nonlinear resonance weakly nonlinear Stokes waves a free surface current rippled beds dynamical system |
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