Re-study on recurrence period of Stokes wave train with high order spectral method |
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| Authors: | Ai-feng Tao Jin-hai Zheng Mee Soe Mee Bo-tao Chen |
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| Institution: | a,b a State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering,Hohai University,Nanjing 210098,China b College of Harbor Coastal and Offshore Engineering,Hohai University,Nanjing 210098,China c Department of Civil Engineering,Myanmar Maritime University,Myanmar |
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| Abstract: | Owing to the Benjamin-Feir instability,the Stokes wave train experiences a modulation-demodulation process,and presents a recurrence characteristics.Stiassnie and Shemer researched the unstable evolution process and provided a theoretical formulation for the recurrence period in 1985 on the basis of the nonlinear cubic Schr dinger equation(NLS).However,NLS has limitations on the narrow band and the weak nonlinearity.The recurrence period is re-investigated in this paper by using a highly efficient High Order Spectral(HOS) method,which can be applied for the direct phaseresolved simulation of the nonlinear wave train evolution.It is found that the Stiassnie and Shemer’s formula should be modified in the cases with most unstable initial conditions,which is important for such topics as the generation mechanisms of freak waves.A new recurrence period formula is presented and some new evolution characteristics of the Stokes wave train are also discussed in details. |
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| Keywords: | Benjamin-Feir instability High Order Spectral(HOS) method recurrence period nonlinear wave-wave interaction |
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