Skip to main content
    • Aa
    • Aa

Low-Reynolds-number fountain behaviour

  • N. WILLIAMSON (a1), N. SRINARAYANA (a1), S. W. ARMFIELD (a1), G. D. McBAIN (a1) and W. LIN (a2)...

Experimental evidence for previously unreported fountain behaviour is presented. It has been found that the first unstable mode of a three-dimensional round fountain is a laminar flapping motion that can grow to a circling or multimodal flapping motion. With increasing Froude and Reynolds numbers, fountain behaviour becomes more disorderly, exhibiting a laminar bobbing motion. The transition between steady behaviour, the initial flapping modes and the laminar bobbing flow can be approximately described by a function FrRe2/3=C. The transition to turbulence occurs at Re > 120, independent of Froude number, and the flow appears to be fully turbulent at Re≈2000. For Fr > 10 and Re≲120, sinuous shear-driven instabilities have been observed in the rising fluid column. For Re≳120 these instabilities cause the fountain to intermittently breakdown into turbulent jet-like flow. For Fr≲10 buoyancy forces begin to dominate the flow and pulsing behaviour is observed. A regime map of the fountain behaviour for 0.7≲Fr≲100 and 15≲Re≲1900 is presented and the underlying mechanisms for the observed behaviour are proposed. Movies are available with the online version of the paper.

Hide All
Abraham G. 1967 Jets with negative buoyancy in homogeneous fluid. J. Hydraul Res. 5, 235248.
Baines W. D., Turner J. S. & Campbell I. H. 1990 Turbulent fountains in an open chamber. J. Fluid Mech. 212, 557592.
Bloomfield L. J. & Kerr R. C. 2000 A theoretical model of a turbulent fountain. J. Fluid Mech.. 424, 197216.
Campbell I. H. & Turner J. S. 1989 Fountains in magma chambers. J. Petrol. 30, 885923.
Clannet C. 1998 On large-amplitude pulsating fountains. J. Fluid Mech. 366, 333350.
Cresswell R. W. & Szczepura R. T. 1993 Experimental investigation into a turbulent jet with negative buoyancy. Phys. Fluids A 5, 28652878.
Friedman P. D. 2006 Oscillation height of a negatively buoyant jet. Trans. ASME J: J. Fluids Engng 128, 880882.
Friedman P. D., Vadokoot V. D., Meyer W. J. & Carey S. 2007 Instability threshold of a negatively buoyant fountain. Exps. Fluids 42, 751759.
Kaminski E., Tait S. & Carazzo G. 2005 Turbulent entrainment in jets with arbitrary buoyancy. J. Fluid Mech. 526, 361376.
Kaye N. B. & Hunt G. R. 2006 Weak fountains. J. F. Mech. 558, 319328.
Lin W. & Armfield S. W. 2000 a Direct simulation of weak axisymmetric fountains in a homogeneous fluid. J. Fluid Mech. 403, 6788.
Lin W. & Armfield S. W. 2000 b Direct simulation of weak laminar plane fountains in a homogeneous fluid. Intl J. Heat Mass Transfer 43, 30133026.
Lin W. & Armfield S. W. 2000 c Very weak axisymmetric fountains in a homogeneous fluid. Numer. Heat Transfer A 38, 377396.
Lin W. & Armfield S. W. 2003 The Reynolds and Prandtl number dependence of weak fountains. Comput. Mech. 31, 379389.
Lin W. & Armfield S. W. 2004 Direct simulation of fountains with intermediate froude and reynolds numbers. ANZIAM J. 45, C66C77.
Middleton J. H. 1975 The asymptotic behavior of a starting plume. J. Fluid Mech. 72, 753771.
Mizushina T., Ogino F., Takeuchi H. & Ikawa H. 1982 An experimental study of vertical turbulent jet with negative buoyancy. Wärme- und Stoffübertragung 16, 1521.
Pantzlaff L. & Lueptow R. M. 1999 Transient positively and negatively buoyant turbulent round jets. Exps. Fluids 27, 117125.
Philippe P., Raufaste C., Kurowski P. & Petitjeans P. 2005 Penetration of a negatively buoyant jet in a miscible liquid. Phys. Fluids 17, 053601.
Srinarayana N., McBain G. D., Armfield S. W. & Lin W. X. 2007 Height and stability of laminar plane fountains in a homogeneous fluid. Intl J. Heat Mass Transfer (submitted).
Turner J. S. 1966 Jets and plumes with negative or reversing buoyancy. J. Fluid Mech. 26, 779792.
Zhang H. & Baddour R. E. 1997 Maximum vertical penetration of plane turbulent negatively buoyant jets. J. Engng Mech. 123, 973977.
Zhang H. & Baddour R. E. 1998 Maximum penetration of vertical round dense jets at small and large Froude numbers. J. Hydraul. Engng 124, 550553.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Type Description Title

Williamson et al. supplementary movie
Movie 2. Visualization of flapping/bobbing behaviour at Re=97 and Fr=1.3, with U0=4.3 cm/s, R0=2.4 mm and Δρ/ρf=0.0459.

 Video (2.9 MB)
2.9 MB

Williamson et al. supplementary movie
Movie 3. Visualization of sinuous behaviour at Re=158 and Fr=45, with U0=28 cm/s, R0=0.565 mm and Δρ/ρf=0.00718.

 Video (490 KB)
490 KB

Williamson et al. supplementary movie
Movie 4. Visualization of sinuous behaviour at Re=26 and Fr=26, with U0=6.9 cm/s, R0=0.38 mm and Δρ/ρf=0.00186.

 Video (1.7 MB)
1.7 MB

Williamson et al. supplementary movie
Movie 5. Visualization of jet breakdown behaviour at Re=152 and Fr=13, with U0=12 cm/s, R0=1.27 mm and Δρ/ρf=0.00718.

 Video (5.2 MB)
5.2 MB

Williamson et al. supplementary movie
Movie 1. Salt-water is injected up into a small fresh water tank. The water is injected from a sudden start and maintained at a constant flow rate throughout the experiment. During an experiment the saline fluid rises and then falls back on itself and finally spreads along the base of the tank. The flow behaviour depends on the Reynolds number and Froude number of the flow. Here visualization of combined flapping and circling behaviour is shown at Re=87.5 and Fr=1.2, with characteristic velocity U0=3.9 cm/s, source radius R0=2.4 mm and density ratio  Δρ/ρf=0.0459. The movie looks down upon the fountain source. Fountain startup behaviour is from 0 to 5 s, two-dimensional flapping exists between 5 and 9 s, circling between 9 and 14 s and two-dimensional flapping behaviour returns again from 14 s onwards.

 Video (4.9 MB)
4.9 MB


Full text views

Total number of HTML views: 1
Total number of PDF views: 77 *
Loading metrics...

Abstract views

Total abstract views: 181 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 21st October 2017. This data will be updated every 24 hours.