Effects of the Varying Bottom on Nonlinear Surface Waves
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摘要: 考虑表面张力的作用，研究了不可压缩、无粘性流体流过变化壁面时的共振流动，分析了不同的底部壁面变化对非线性表面波的影响．在导出非线性表面波遵循的fKdV方程后，利用拟谱方法进行数值模拟，用Matlab软件绘制瀑布图，由此得出结论：上凸底部上的波可以看成是向前凸台阶和向后凸台阶分别向前后散射发展的结果，二者不发生相互作用；下凹壁面的波形是向前凹台阶和向后凹台阶相互作用的结果；某些组合式底部的波形是上凸和下凹相互作用的结果．Abstract: The resonant flow of an incompressible,inviscid fluid with surface tension on varying bottoms was researched.The effects of different bottoms on the nonlinear surface waves were analyzed.The waterfall plots of the wave were drawn with Matlab according to the numerical simulation of the fKdV equation with the pseudo-spectral method.From the waterfall plots,the results are obtained as follows:for the convex bottom,the waves system can be viewed as a combination of the effects of forward-step forcing and backward-step forcing,and these two wave systems respectively radiate upstream and downstream without mutual interaction.Nevertheless,the result for the concave bottom is contrary to the convex one.For some combined bottoms,the wave systems can be considered as the combination of positive forcing and negative forcing.
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Key words:
- varying bottom /
- resonant flow /
- solitary wave /
- fKdV equation /
- pseudo-spectral method /
- waterfall plot
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[1] Kapitza P L，Kapitza S P.Wave flow of thin layers of a viscous fluid[A].In:Haar D Ter Ed.Collected Papers of P L Kapitza(Vol.Ⅱ)[C].New York：The Macmillan Company, 1964，662—709. [2] 蒋章焰，马同泽，赵嘉琅,等.垂直管外降落液膜的流动和传热特性[J].工程热物理学报，1988，9（1）：70—74. [3] Lin S P，Wang C Y.Modeling wavy film flows[A].In:Cheremisinoff N P Ed.Encyclopedia of Fluid Mechanics[C].Houston: Gulf Publishing Co,1986,930—951. [4] Akylas T R.On the excitation of long nonlinear water waves by a moving pressure distribution[J].J Fluid Mech，1984，141：455—466. doi: 10.1017/S0022112084000926 [5] Wang C Y.Liquid film flowing slowly down a wavy incline[J].American Institute of Chemical Engineering,1981，27（2）：207—212. doi: 10.1002/aic.690270206 [6] Davis A G，Heathershaw A D.Surface-wave propagation over sinusoidally varying topography[J].J Fluid Mech，1984，144：419—443. doi: 10.1017/S0022112084001671 [7] ZHANG Dao-hua，Chwang Allen T.Generation of solitary waves by forward- and backward-step bottom forcing[J].J Fluid Mech，2001，432：341—350. [8] Yoshimasa Nonaka.Internal solitary waves moving over the low slope of topographies[J].Fluid Dynamics Research，1996，17（6）：329—349. doi: 10.1016/0169-5983(95)00035-6 [9] 朱勇.流体流过下凹地形的共振流动[J].应用数学和力学，1997，18（5）：447—450. [10] Fornberg B，Whitham G B.A numerical and theoretical study of certain nonlinear wave phenomena[J].J Fluid Mech,1978,289:333—404. [11] Fornberg Bengt.A Practical Guide to Pseudospectral Methods[M].New York：Cambridge University Press, 1996，173—196. [12] Wu T Y.Generation of upstream advancing solitons by moving disturbance[J].J Fluid Mech，1984，184：75—99. -
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