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The rhythm of fountains: the length and time scales of rise height fluctuations at low and high Froude numbers

Published online by Cambridge University Press:  01 July 2013

H. C. Burridge
Affiliation:
Department of Civil and Environmental Engineering, Imperial College London, Imperial College Road, London SW7 2AZ, UK
G. R. Hunt*
Affiliation:
Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK
*Corresponding
Email address for correspondence: gary.hunt@eng.cam.ac.uk

Abstract

The magnitude and frequency of vertical fluctuations of the top of an axisymmetric miscible Boussinesq fountain forms the focus of this work. We present measurements of these quantities for saline-aqueous fountains in uniform quiescent surroundings. Our results span source Froude numbers $0. 3\leq {\mathrm{Fr} }_{0} \leq 40$ and, thereby, encompass very weak, weak, intermediate and forced classes of fountain. We identify distinct scalings, based on known quantities at the fountain source, for the frequency of fountain height fluctuations which collapse our data within bands of ${\mathrm{Fr} }_{0} $ . Notably, our scalings reveal that the (dimensionless) frequency takes a constant value within each band. These results highlight characteristic time scales for the fluctuations which we decompose into a single, physically apparent, length scale and velocity scale within each band. Moreover, within one particular band, spanning source Froude numbers towards the lower end of the full range considered, we identify unexpectedly long-period fluctuations indicating a near balance of inertia and (opposing) buoyancy at the source. Our analysis identifies four distinct classes of fluctuation behaviour (four bands of ${\mathrm{Fr} }_{0} $ ) and this classification matches well with existing classifications of fountains based on rise heights. As such, we show that an analysis of the behaviour of the fountain top alone, rather than the entire fountain, provides an alternative approach to classifying fountains. The similarity of classifications based on the two different methods confirms that the boundaries between classes mark tangible changes in the physics of fountains. For high ${\mathrm{Fr} }_{0} $ we show that the dominant fluctuations occur at the scale of the largest eddies which can be contained within the fountain near its top. Extending this, we develop a Strouhal number, ${\mathrm{Str} }_{top} $ , based on experimental measures of the fountain top, defined such that ${\mathrm{Str} }_{top} = 1$ would suggest the dominant fluctuations are caused by a continual cycle of eddies forming and collapsing at this largest physical scale. For high- ${\mathrm{Fr} }_{0} $ fountains we find ${\mathrm{Str} }_{top} \approx 0. 9$ .

Type
Papers
Copyright
©2013 Cambridge University Press 

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References

Baines, W. D., Corriveau, A. F. & Reedman, T. J. 1993 Turbulent fountains in a closed chamber. J. Fluid Mech. 255, 621646.CrossRefGoogle Scholar
Baines, W. D., Turner, J. S. & Campbell, I. H. 1990 Turbulent fountains in an open chamber. J. Fluid Mech. 212, 557592.CrossRefGoogle Scholar
Bloomfield, L. J. & Kerr, R. C. 2000 A theoretical model of a turbulent fountain. J. Fluid Mech. 424, 197216.CrossRefGoogle Scholar
Burridge, H. C. & Hunt, G. R. 2012 The rise heights of low- and high-Froude-number turbulent axisymmetric fountains. J. Fluid Mech. 691, 392416.CrossRefGoogle Scholar
Clanet, C. 1998 On large-amplitude pulsating fountains. J. Fluid Mech. 366, 333350.CrossRefGoogle Scholar
Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J. & Brooks, N. H. 1979 Mixing in Inland and Coastal Waters. Academic.Google Scholar
Friedman, P. D. 2006 Oscillation in height of a negatively buoyant jet. Trans. ASME: J. Fluids Engng 128, 880882.Google Scholar
Kaminski, E., Tait, S. & Carazzo, G. 2005 Turbulent entrainment in jets with arbitrary buoyancy. J. Fluid Mech. 526, 361376.CrossRefGoogle Scholar
Kaye, N. B. & Hunt, G. R. 2006 Weak fountains. J. Fluid Mech. 558, 319328.CrossRefGoogle Scholar
Lin, W. & Armfield, S. W. 2000 Very weak fountains in a homogeneous fluid. Numer. Heat Transfer A 38, 377396.Google Scholar
Mizushina, T., Ogino, F., Takeuchi, H. & Ikawa, H. 1982 An experimental study of vertical turbulent jet with negative buoyancy. Heat Mass Transfer 16, 1521.Google Scholar
Myrtroeen, O. J. & Hunt, G. R. 2012 On the transition from finite-volume negatively buoyant releases to continuous fountains. J. Fluid Mech. 698, 168184.CrossRefGoogle Scholar
Savitzky, A. & Golay, M. J. E. 1964 Smoothing and differentiation of data by simplified least squares procedures. Analyt. Chem. 36, 16271639.CrossRefGoogle Scholar
Spiegel, E. A. & Veronis, G. 1960 On the Boussinesq approximation for compressible fluids. Astrophys. J. 131, 442447.CrossRefGoogle Scholar
Turner, J. S. 1966 Jets and plumes with negative or reversing buoyancy. J. Fluid Mech. 26, 779792.CrossRefGoogle Scholar
Williamson, N., Armfield, S. W. & Lin, W. 2010 Transition behaviour of weak turbulent fountains. J. Fluid Mech. 655, 306326.CrossRefGoogle Scholar
Williamson, N., Srinarayana, N., Armfield, S. W., McBain, G. D. & Lin, W. 2008 Low-Reynolds-number fountain behaviour. J. Fluid Mech. 608, 297317.CrossRefGoogle Scholar
Zhang, H. & Baddour, R. E. 1998 Maximum penetration of vertical round dense jets at small and large Froude numbers. J. Hydraul. Engng 124, 550553.CrossRefGoogle Scholar
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The rhythm of fountains: the length and time scales of rise height fluctuations at low and high Froude numbers
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