Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-22T08:40:33.309Z Has data issue: false hasContentIssue false
  • English
  • Français

Experimental studies of surface waves inside a cylindrical container

Published online by Cambridge University Press:  09 May 2011

CUNBIAO LEE ,
HUAIWU PENG ,
HUIJING YUAN ,
JIEZHI WU ,
MINGDE ZHOU  and
FAZLE HUSSAIN
CUNBIAO LEE*
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China
HUAIWU PENG
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China
HUIJING YUAN
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China
JIEZHI WU
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China
MINGDE ZHOU
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China
FAZLE HUSSAIN
Affiliation:
Department of Mechanical Engineering, University of Houston, Houston, TX 77204 4006, USA
*
†Email address for correspondence: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We experimentally investigate the dynamics of surface waves excited by oscillations from a cylindrical sidewall. Particle-imaging-velocimetry measurements with fluorescent particles were used to determine the flow patterns near the sidewall of the cylindrical fluid container and to identify the locations of the evolving air–water interfaces. The high-frequency wall oscillations created four jets that originate at the cylindrical sidewall. Four vortex streets shed from the jets propagate from the sidewall to the centre of the container and subsequently excite a low-frequency gravity wave. The interaction between this gravitational surface wave and the high-frequency capillary waves was found to be responsible for creating droplet splash at the water surface. This phenomenon was first described as ‘Long-Xi’ or ‘dragon wash’ in ancient China. The physical processes for generating the droplet ejection, including the circular capillary waves, azimuthal waves, streaming jets and low-frequency gravity waves, are described in this paper.

JFM classification

Waves/Free-surface Flows: Capillary waves Instability: Instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 677 , 25 June 2011 , pp. 39 - 62
Copyright
Copyright © Cambridge University Press 2011. The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution-NonCommercial-ShareAlike licence <http://creativecommons.org/licenses/by-nc-sa/2.5/>. The written permission of Cambridge University Press must be obtained for commercial re-use.

References

REFERENCES

Carlsson, F., Sen, M. & Löfdahl, L. 2004 Steady streaming due to vibrating walls. Phys. Fluids 16, 2375–2395.CrossRefGoogle Scholar
Chang, C. C. 1999 Nonlinear theories of forced surface waves in a circular basin. PhD thesis, University of Wisconsin-Madison, Madison, WI.Google Scholar
Chang, C. C. & Shen, M. C. 2000 a Chaotic motion and internal resonance of forced surface waves in a water-filled circular basin. Wave Motion 31, 317–331.CrossRefGoogle Scholar
Chang, C. C. & Shen, M. C. 2000 b Nonlinear capillary–gravity waves under an edge condition. J. Engng Math. 38, 391–402.CrossRefGoogle Scholar
Davidson, B. J. & Riley, N. 1972 Jets induced by oscillatory motion. J. Fluid Mech. 53, 287–303.CrossRefGoogle Scholar
Faltinsen, O. M., Rognebakke, O. F. & Timokha, A. N. 2006 a Resonant three-dimensional nonlinear sloshing in a square-base basin. Part 3. Base ratio perturbations. J. Fluid Mech. 551, 93–116.CrossRefGoogle Scholar
Faltinsen, O. M., Rognebakke, O. F. & Timokha, A. N. 2006 b Transient and steady-state amplitudes of resonant three-dimensional sloshing in a square-based tank with a finite fluid depth. Phys. Fluids 18, 012103.CrossRefGoogle Scholar
Faraday, M. 1831 On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces. Philos. Trans. R. Soc. Lond. 121, 299–340.Google Scholar
Fukaya, M., Madarame, H. & Okamoto, K. 1996 Growth mechanism of self-induced sloshing caused by jet in rectangular tank (2nd report, multimode sloshing caused by horizontal rectangular jet). Trans. JSME, (B) 62, 64–71.Google Scholar
Gavrilyuk, I., Lukovsky, I. & Timokha, A. 2004 Two-dimensional variational vibroequilibria and Faraday's drops. Z. Angew. Math. Phys. 55, 1015–1033.CrossRefGoogle Scholar
Goodridge, C. L., Shi, W. T. & Lathrop, D. P. 1996 Threshold dynamics of singular gravity–capillary waves. Phys. Rev. Lett. 76, 1824–1827.CrossRefGoogle ScholarPubMed
Hirsa, A. H., Lopez, J. M. & Miraghaie, R. 2002 Determination of surface shear viscosity via deep-channel flow with inertia. J. Fluid Mech. 470, 135–149.CrossRefGoogle Scholar
Ho, C. M. & Huerre, P. 1984 Perturbed free shear layers. Annu. Rev. Fluid Mech. 16, 365–424.CrossRefGoogle Scholar
Hsieh, D. Y. 1994 Standing water waves in a circular basin. In Proceedings of the International Conference on Hydrodynamics, pp. 74–79.Google Scholar
Hsieh, D. Y. 1997 Water waves in an elastic vessel. Acta Mechanica Sin. 13, 289–303.CrossRefGoogle Scholar
Hsieh, D. Y. 2000 Theory of water waves in an elastic vessel. Acta Mechanica Sin. 16, 97–112.CrossRefGoogle Scholar
Hsieh, D. Y. & Denissenko, P. 1998 Water waves in a circular elastic vessel: the experiment. Tech. Rep. 98-6-1. Department of Mathematics, Hong Kong University of Science and Technology.Google Scholar
Hu, H., Kobayashi, T., Saga, T., Segawa, T. N., Taniguchi, N. M. & Okamoto, K. 1999 A PIV study on the self-induced sloshing in a tank with circulating flow. In Second Pacific Symposium on Flow Visualization and Image Processing, CD-ROM paper No. PF152.Google Scholar
Huntley, I. 1972 Observations on a spatial-resonance phenomenon. J. Fluid Mech. 53, 209–216.CrossRefGoogle Scholar
Jenkins, A. D. & Dysthe, K. B. 1997 The effective film viscosity coefficients of a thin floating fluid layer. J. Fluid Mech. 344, 335–337.CrossRefGoogle Scholar
Lee, C. B. & Wu, J. Z. 2008 Transition in wall-bounded flow. Appl. Mech. Rev. 61, 030802.CrossRefGoogle Scholar
Lighthill, M. J. 1978 Acoustic streaming. J. Sound Vib. 61, 391–418.CrossRefGoogle Scholar
Lin, H. J. & Perlin, M. 2001 The velocity and vorticity fields beneath gravity–capillary waves exhibiting parasitic ripples. Wave Motion 33, 245–257.CrossRefGoogle Scholar
Liu, X. J., Liu, G. Y., Jia, Q. F. & Zhang, S. X. 2005 Vibration analysis of the revolving gravity waves in fluid-filled cylindrical shells. J. Tianjin Univ. Sci. Techol. 38, 288–293.Google Scholar
Mahony, J. J. & Smith, R. 1972 On a model representation for the spatial-resonance phenomena. J. Fluid Mech. 53, 193–207.CrossRefGoogle Scholar
Miles, J. & Henderson, D. 1990 Parametrically forced surface waves. Annu. Rev. Fluid Mech. 22, 143–165.CrossRefGoogle Scholar
Mui, R. C. Y. & Dommermuth, D. G. 1995 The vortical structure of parasitic capillary waves. J. Fluid Engng 117, 355–361.CrossRefGoogle Scholar
Okamoto, K., Madarame, H. & Hagiwara, T. 1991 Self-induced oscillation of free surface in a tank with circulating flow. In Proc. Fifth Intl Conf. Flow Induced Vibrations (ed. Clarkson, B. L.), pp. 539–545. IMechE.Google Scholar
Peng, H. W. & Lee, C. B. 2009 Periodic tripling and jet eruption of forced steep gravity waves. Mod. Phys. Lett. B 23, 397–400.CrossRefGoogle Scholar
Peng, H. W., Li, R. Q., Chen, S. Z. & Lee, C. B. 2008 Correlation dimension analysis and capillary wave turbulence in dragon-wash phenomena. Chin. Phys. B 17, 637–643.Google Scholar
Peng, H. W., Wang, D. J. & Lee, C. B. 2005 Nonlinear low frequency water waves in a cylindrical shell. Mod. Phys. Lett. B 19, 1615–1618.CrossRefGoogle Scholar
Peng, H. W., Yuan, H. J., Chen, S. Z., Wang, D. J. & Lee, C. B. 2006 Experimental studies on dragon wash phenomena. J. Hydrodyn. 18, 507–510.CrossRefGoogle Scholar
Rayleigh, L. 1883 On the circulation of air observed in Kundts tubes and some allied acoustical problems. Philos. Trans. R. Soc. Lond. Ser. A 175, 1–21.Google Scholar
Riley, N. 2001 Steady streaming. Annu. Rev. Fluid Mech. 33, 43–65.CrossRefGoogle Scholar
Royon-Lebeaud, A. Hopfinger, E. J. & Cartellier, A. 2007 Liquid sloshing and wave breaking in circular and square-base cylindrical containers. J. Fluid Mech. 577, 467–494.CrossRefGoogle Scholar
Saeki, S., Madarame, H. & Okamoto, K. 2001 Self-induced sloshing excited by a horizontally injected plane jet. J. Fluid Mech. 448, 81–114.CrossRefGoogle Scholar
Saeki, S., Madarame, H., Okamoto, K. & Tanaka, N. 1997 Numerical study on the self-induced sloshing. In FEDSM97-3401 ASME FED Summer Meeting.Google Scholar
Sharipov, F. M. & Kremer, G. M. 1999 Non-isothermal Couette flow of a rarefied gas between two rotating cylinders. Eur. J. Mech. B/Fluids 18, 121–130.CrossRefGoogle Scholar
Shen, M. C. & Hsieh, D. Y. 1993 Forced capillary–gravity waves in a circular basin. Wave Motion 18, 401–412.CrossRefGoogle Scholar
Shen, M. C. & Yeh, N. S. 1997 Exact solution for forced capillary–gravity waves in a circular basin under Hocking's edge condition. Wave Motion 26, 117–126.CrossRefGoogle Scholar
Sun, S. M., Shen, M. C. & Hsieh, D. Y. 1995 Nonlinear theory of forced surface waves in a circular basin. Wave Motion 21, 331–341.CrossRefGoogle Scholar
Takizawa, A., Koshizuka, S. & Kondo, S. 1992 Generalization of physical components boundary fitted coordinate (PCBFC) method for the analysis of free surface flow. Intl J. Numer. Meth. Fluids 15, 1213–1237.CrossRefGoogle Scholar
Tower, D. P., Towers, C. E., Buckberry, C. H. & Reeves, M. 1999 A colour PIV system employing fluorescent particles for two-phase flow measurements. Meas. Sci. Technol. 10, 824–830.CrossRefGoogle Scholar
Wang, D. J. 1993 Study on mechanical characteristics of ancient cultural relics. Sci. Conserv. Archaeol. 5, 35–39.Google Scholar
Wang, D. J. 2005 Bell chime, dragon washbasin—modern scientific information hidden in ancient Chinese science and technology. Technishe Mechanik 25, 9–16.Google Scholar
Wei, Q., Wang, D., Yan, B., Du, X. & Chen, J. 1997 A visualization study on water spray of dragon washbasin. In Atlas of Visualization (ed. The Visualization Society of Japan), pp. 169–179. CRC press.Google Scholar
Welsh, M. C., Stokes, A. N. & Parker, R. 1984 Flow-resonant sound interaction in a duct containing a plate. Part 1. Semicircular leading edge. J. Sound Vib. 95, 305–323.CrossRefGoogle Scholar
Wu, J. Z. 1995 A theory of three-dimensional interfacial vorticity dynamics. Phys. Fluids 7, 2375–2395.CrossRefGoogle Scholar
Wu, J. Z., Ma, H. Y. & Zhou, M. D. 2006 Vorticity and Vortex Dynamics. Springer-Verlag.CrossRefGoogle Scholar