NONLINEAR FARADAY WAVES IN A PARAMETRICALLY EXCITED CIRCULAR CYLINDRICAL CONTAINER

Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (10): 1194-1207.

NONLINEAR FARADAY WAVES IN A PARAMETRICALLY EXCITED CIRCULAR CYLINDRICAL CONTAINER

菅永军^1,2, 鄂学全¹, 柏威¹

1. Department of Engineering Science, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, P. R. China;
2. First Institute of Oceanography, State Oceanic Administration, Qingdao, Shandong 266061, P. R. China

收稿日期:2003-03-30 修回日期:2003-05-16 出版日期:2003-10-18 发布日期:2003-10-18
基金资助:
the National Natural Science Foundation of China (19772063, 19772068)

NONLINEAR FARADAY WAVES IN A PARAMETRICALLY EXCITED CIRCULAR CYLINDRICAL CONTAINER

JIAN Yong-jun^1,2, E Xue-quan¹, BAI Wei¹

1. Department of Engineering Science, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, P. R. China;
2. First Institute of Oceanography, State Oceanic Administration, Qingdao, Shandong 266061, P. R. China

Received:2003-03-30 Revised:2003-05-16 Online:2003-10-18 Published:2003-10-18
Supported by:
the National Natural Science Foundation of China (19772063, 19772068)

摘要/Abstract

摘要： 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.

Abstract: 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.

中图分类号:

O353.2

菅永军;鄂学全;柏威. NONLINEAR FARADAY WAVES IN A PARAMETRICALLY EXCITED CIRCULAR CYLINDRICAL CONTAINER[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(10): 1194-1207.

JIAN Yong-jun;E Xue-quan;BAI Wei. NONLINEAR FARADAY WAVES IN A PARAMETRICALLY EXCITED CIRCULAR CYLINDRICAL CONTAINER[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(10): 1194-1207.

参考文献

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NONLINEAR FARADAY WAVES IN A PARAMETRICALLY EXCITED CIRCULAR CYLINDRICAL CONTAINER

NONLINEAR FARADAY WAVES IN A PARAMETRICALLY EXCITED CIRCULAR CYLINDRICAL CONTAINER

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