参数激励圆柱形容器中的非线性Faraday波  

Nonlinear Faraday Waves in a Parametrically Excited Circular Cylindrical Container

作　　者：菅永军[1] 鄂学全[1] 柏威[1] 

机构地区：[1]中国科学院力学研究所工程科学部

出　　处：《应用数学和力学》2003年第10期1057-1068,共12页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(19772063;19772068)

摘　　要：　在柱坐标系下,通过奇异摄动理论的多尺度展开法求解势流方程,研究了垂直强迫激励圆柱形容器中的单一模式水表面驻波模式·　假设流体是无粘、不可压且运动是无旋的,在忽略了表面张力的影响下,用两变量时间展开法得到一个具有立方项以及底部驱动项影响的非线性振幅方程·　对上述方程进行了数值计算,计算的结果显示了在不同驱动振幅和驱动频率下,会激发不同自由水表面驻波模式,从等高线的图像来看。In the cylindrical coordinate system,a singular perturbation theory of multiple_scale asymptotic expansions was developed to study single standing water wave mode by solving potential equations of water waves in a rigid circular cylinder, which is subject to a vertical oscillation.It is assumed that the fluid in the circular cylindrical vessel is inviscid,incompressible and the motion is irrotational, a nonlinear amplitude equation with cubic and vertically excited terms of the vessel was derived by expansion of two_time scales without considering the effect of surface tension.It is shown by numerical computation that different free surface standing wave patterns will be formed in different excited frequencies and amplitudes.The contours of free surface waves are agreed well with the experimental results which were carried out several years ago.

关 键 词：垂直强迫振动 非线性 Famday波 奇异摄动展开 振幅方程 

分 类 号：O353.2[理学—流体力学]