Damping of Vertically Excited Surface Wave in a Weakly Viscous Fluid

JIAN Yong-jun; E Xue-quan; ZHANG Jie

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Article Navigation > Applied Mathematics and Mechanics > 2006 > 27(3): 372-378

JIAN Yong-jun, E Xue-quan, ZHANG Jie. Damping of Vertically Excited Surface Wave in a Weakly Viscous Fluid[J]. Applied Mathematics and Mechanics, 2006, 27(3): 372-378.

Citation:

JIAN Yong-jun, E Xue-quan, ZHANG Jie. Damping of Vertically Excited Surface Wave in a Weakly Viscous Fluid[J]. Applied Mathematics and Mechanics, 2006, 27(3): 372-378.

Citation:

JIAN Yong-jun, E Xue-quan, ZHANG Jie. Damping of Vertically Excited Surface Wave in a Weakly Viscous Fluid[J]. Applied Mathematics and Mechanics, 2006, 27(3): 372-378.

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Damping of Vertically Excited Surface Wave in a Weakly Viscous Fluid

1.
First Institute of Oceanography, State Oceanic Administration, Qingdao 266061, P. R. China;

Received Date: 2004-06-09
Rev Recd Date: 2005-10-16
Publish Date: 2006-03-15

Abstract

Abstract

In a vertically oscillating circular cylindrical container,singular perturbation theory of two-time scale expansions was developed in weakly viscous fluids to investigate the motion of single free surface standing wave by linearizing the Navier-Stokes equation.The fluid field was divided into an outer potential flow region and an inner boundary layer region.The solutions of both two regions were obtained and a linear amplitude equation incorporating damping term and external excitation was derived.The condition to appear stable surface wave was obtained and the critical curve was determined.In addition,an analytical expression of damping coefficient was determined.Finally,the dispersion relation,which has been derived from the inviscid fluid approximation,is modified by adding linear damping.It is found that the modified results are more reasonably close to experimental results.Result shows that when forcing frequency is low,the viscosity of the fluid is prominent for the mode selection.However,when forcing frequency is high,the surface tension of the fluid is prominent.
- vertically forced oscillation,
- viscous damping,
- weakly viscous fluid

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References(9)

References

[1]	E Xue-quan,GAO Yu-xin.Ordered and chaotic modes of surface wave patterns in a vertically oscillating fluid[J].Communications in Nonlinear Sciences & Numerical Simulation,1996,1(2):1—6.
[2]	E Xue-quan,GAO Yu-xin.Visualization of surface wave patterns of a fluid in vertical vibration[A].In:Proceedings of the Fourth Asian Symposium on Visualization[C].Beijing:International Academic Publishers,1996,653—658.
[3]	高宇欣，鄂学全.微幅振荡流体表面波图谱显示方法[J].实验力学，1998,13(3):326—333.
[4]	菅永军，鄂学全，柏威.参数激励圆柱形容器中的非线性Faraday波[J].应用数学和力学,2003,24(10):1057—1068.
[5]	菅永军，鄂学全.垂直激励圆柱形容器中的表面波结构[J].水动力学研究与进展,2003,18(2):135—147.
[6]	菅永军，鄂学全，张杰.圆柱形容器中竖直激励表面波的毛细影响[J].应用数学和力学,2006,27(2):204—210.
[7]	菅永军，鄂学全.刚性充液容器内竖直激励表面波研究进展[J].力学进展，2004，34(1):61—76.
[8]	Hill D F. The Faraday resonance of interfacial waves in weakly viscous fluids[J].Physics of Fluids,2002,14(1):158—169. doi: 10.1063/1.1425846
[9]	Henderson D M. Effects of surfactants on Faraday-wave dynamics[J].Journal of Fluid Mechanics,1998,365(12):89—107. doi: 10.1017/S0022112098001086