NONLINEAR FARADAY WAVES IN A PARAMETRICALLY EXCITED CIRCULAR CYLINDRICAL CONTAINER

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

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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)

Abstract

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.

2010 MSC Number:

O353.2

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

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NONLINEAR FARADAY WAVES IN A PARAMETRICALLY EXCITED CIRCULAR CYLINDRICAL CONTAINER

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