1932

Abstract

Turbulent fountains arise when a localized flow, free to entrain fluid from its surroundings, is opposed by a buoyancy force. This review cites numerous examples to highlight their wide occurrence in nature and in industry. The breadth of the literature reviewed is significant, drawing from over half a century of progress, and we initially focus on axisymmetric, small–density difference fountains in uniform environments. Many aspects of their rich dynamical behavior, including that of their rise heights and fluctuations in height, are described and encapsulated within the fountain classification presented. Drawing from detailed experimental data sets, dimensional considerations, recent numerical studies, and numerous successful extensions to the original theoretical model for a fountain, we implicitly highlight the current predictive capability offered. The turbulent entrainment of ambient fluid, the effects of environmental stratification, and the role of confinement on a fountain are all discussed. Finally, we suggest future avenues of research.

Associated Article

There are media items related to this article:
Fountains in Industry and Nature: Supplemental Video 1
Loading

Article metrics loading...

/content/journals/10.1146/annurev-fluid-010313-141311
2015-01-03
2024-04-27
Loading full text...

Full text loading...

/deliver/fulltext/fluid/47/1/annurev-fluid-010313-141311.html?itemId=/content/journals/10.1146/annurev-fluid-010313-141311&mimeType=html&fmt=ahah

Literature Cited

  1. Abraham G. 1967. Jets with negative buoyancy in homogeneous fluid. J. Hydraul. Res. 5:235–48 [Google Scholar]
  2. Abramovich GN. 1963. The Theory of Turbulent Jets Cambridge, MA: MIT Press
  3. Ai J, Law AWK, Yu SCM. 2006. On Boussinesq and non-Boussinesq starting forced plumes. J. Fluid Mech. 558:357–86 [Google Scholar]
  4. Alpert RL. 1975. Turbulent ceiling-jet induced by large-scale fires. Combust. Sci. Technol. 11:197–213 [Google Scholar]
  5. Ansong JK, Anderson-Frey A, Sutherland BR. 2011. Turbulent fountains in one- and two-layer crossflows. J. Fluid Mech. 689:254–78 [Google Scholar]
  6. Baddour RE, Zhang H. 2009. Density effect on round turbulent hypersaline fountain. J. Hydraul. Eng. 135:57–59 [Google Scholar]
  7. Baines WD. 1975. Entrainment by a plume or jet at a density interface. J. Fluid Mech. 68:309–20 [Google Scholar]
  8. Baines WD, Corriveau AF, Reedman TJ. 1993. Turbulent fountains in a closed chamber. J. Fluid Mech. 255:621–46 [Google Scholar]
  9. Baines WD, Turner JS. 1969. Turbulent buoyant convection from a source in a confined region. J. Fluid Mech. 37:51–80 [Google Scholar]
  10. Baines WD, Turner JS, Campbell IH. 1990. Turbulent fountains in an open chamber. J. Fluid Mech. 212:557–92 [Google Scholar]
  11. Barnett SJ. 1991. The dynamics of buoyant releases in confined spaces PhD Thesis, Dep. Appl. Math. Theor. Phys., Univ. Cambridge
  12. Bloomfield LJ, Kerr RC. 1998. Turbulent fountains in a stratified fluid. J. Fluid Mech. 358:335–56 [Google Scholar]
  13. Bloomfield LJ, Kerr RC. 1999. Turbulent fountains in a confined stratified environment. J. Fluid Mech. 389:27–54 [Google Scholar]
  14. Bloomfield LJ, Kerr RC. 2000. A theoretical model of a turbulent fountain. J. Fluid Mech. 424:197–216 [Google Scholar]
  15. Bloomfield LJ, Kerr RC. 2002. Inclined turbulent fountains. J. Fluid Mech. 451:283–94 [Google Scholar]
  16. Burridge HC, Hunt GR. 2012. The rise heights of low- and high-Froude-number turbulent axisymmetric fountains. J. Fluid Mech. 691:392–416 [Google Scholar]
  17. Burridge HC, Hunt GR. 2013. The rhythm of fountains: the length and time scales of rise height fluctuations at low and high Froude numbers. J. Fluid Mech. 728:91–119 [Google Scholar]
  18. Burridge HC, Hunt GR. 2014. Scaling arguments for the fluxes in turbulent miscible fountains. J. Fluid Mech. 744:273–85 [Google Scholar]
  19. Burridge HC, Mistry A, Hunt GR. 2014. The effect of source Reynolds number on the rise height of a fountain. Phys. Fluids Submitted manuscript
  20. Campbell IH, Turner JS. 1989. Fountains in magma chambers. J. Petrol. 30:885–923 [Google Scholar]
  21. Carazzo G, Kaminski E, Tait S. 2006. The route to self-similarity in turbulent jets and plumes. J. Fluid Mech. 547:137–48 [Google Scholar]
  22. Carazzo G, Kaminski E, Tait S. 2010. The rise and fall of turbulent fountains: a new model for improved quantitative predictions. J. Fluid Mech. 657:265–84 [Google Scholar]
  23. Cardoso SSS, McHugh ST. 2010. Turbulent plumes with heterogeneous chemical reaction on the surface of small buoyant droplets. J. Fluid Mech. 642:49–77 [Google Scholar]
  24. Cardoso SSS, Woods AW. 1993. Mixing by a turbulent plume in a confined stratified region. J. Fluid Mech. 250:277–305 [Google Scholar]
  25. Carlotti P, Hunt GR. 2005. Analytical solutions for turbulent non-Boussinesq plumes. J. Fluid Mech. 538:343–59 [Google Scholar]
  26. Ching CY, Fernando HJS, Noh Y. 1993. Interaction of a negatively buoyant line plume with a density interface. Dyn. Atmos. Oceans 19:367–88 [Google Scholar]
  27. Clanet C. 1998. On large-amplitude pulsating fountains. J. Fluid Mech. 366:333–50 [Google Scholar]
  28. Coffey CJ, Hunt GR. 2010. The unidirectional emptying box. J. Fluid Mech. 660:456–74 [Google Scholar]
  29. Cooper LY. 1988. Ceiling jet-driven wall flows in compartment fires. Combust. Sci. Technol. 62:285–96 [Google Scholar]
  30. Cooper P, Hunt GR. 2007. Impinging axisymmetric turbulent fountains. Phys. Fluids 19:117101 [Google Scholar]
  31. Cooper P, Hunt GR. 2010. The ventilated filling box containing a vertically distributed source of buoyancy. J. Fluid Mech. 646:39–58 [Google Scholar]
  32. Crapper PF, Baines WD. 1977. Non Boussinesq forced plumes. Atmos. Environ. 11:415–20 [Google Scholar]
  33. Cresswell RW, Szczepura RT. 1993. Experimental investigation into a turbulent jet with negative buoyancy. Phys. Fluids A 11:2865–78 [Google Scholar]
  34. Darcy H. 1856. Les Fontaines Publiques de la Ville de Dijon Paris: Dalmont
  35. Davies PA, Käse RH, Ahmed I. 2001. Laboratory and numerical model studies of a negatively-buoyant jet discharged horizontally into a homogeneous rotating fluid. Geophys. Astrophys. Fluid Dyn. 95:127–83 [Google Scholar]
  36. Devenish BJ, Rooney GG, Thomson DJ. 2010. Large-eddy simulation of a buoyant plume in uniform and stably stratified environments. J. Fluid Mech. 652:75–103 [Google Scholar]
  37. Fernando HJS. 1991. Turbulent mixing in stratified fluids. Annu. Rev. Fluid Mech. 23:455–93 [Google Scholar]
  38. Fox DG. 1970. Forced plume in a stratified fluid. J. Geophys. Res. 75:6818–35 [Google Scholar]
  39. Friedman PD. 2006. Oscillation in height of a negatively buoyant jet. ASME J. Fluids Eng. 128:880–82 [Google Scholar]
  40. Friedman PD, Katz J. 2000. Rise height for negatively buoyant fountains and depth of penetration for negatively buoyant jets impinging an interface. ASME J. Fluids Eng. 122:779–82 [Google Scholar]
  41. Friedman PD, Vadakoot VD, Meyer WJ, Carey S. 2007. Instability threshold of a negatively buoyant fountain. Exp. Fluids 42:751–59 [Google Scholar]
  42. Gharib M, Rambod E, Shariff K. 1998. A universal time scale for vortex ring formation. J. Fluid Mech. 360:121–40 [Google Scholar]
  43. Giannakopoulos BA, Kaye NB, Hunt GR. 2013. The influence of room geometry and overturning of smoke due to a floor fire. Proc. ICE Eng. Comput. Mech. 166:68–87 [Google Scholar]
  44. Gladstone C, Woods AW. 2001. On buoyancy-driven natural ventilation of a room with a heated floor. J. Fluid Mech. 441:293–314 [Google Scholar]
  45. Goldman D, Jaluria Y. 1986. Effect of opposing buoyancy on the flow in free and wall jets. J. Fluid Mech. 166:41–56 [Google Scholar]
  46. Guyonnaud L, Solliec C, Dufresne de Virel M, Rey C. 2000. Design of air curtains used for area confinement in tunnels. Exp. Fluids 28:377–84 [Google Scholar]
  47. Horace 1916 (23 bc). To the fountain of Bandusia. The Poems of Eugene Field transl. E. Field 353–54 New York: Scribner's [Google Scholar]
  48. Hunt GR, Coffey CJ. 2009. Characterising line fountains. J. Fluid Mech. 623:317–27 [Google Scholar]
  49. Hunt GR, Cooper P, Linden PF. 2001. Thermal stratification produced by plumes and jets in enclosed spaces. Build. Environ. 36:871–82 [Google Scholar]
  50. Hunt GR, Kaye NB. 2005. Lazy plumes. J. Fluid Mech. 533:329–38 [Google Scholar]
  51. Jaluria Y, Kapoor K. 1992. Wall and corner flows driven by a ceiling jet in an enclosure fire. Combust. Sci. Technol. 86:311–26 [Google Scholar]
  52. Jeon GY, Kim JY, Hong WH, Augenbroe G. 2011. Evacuation performance of individuals in different visibility conditions. Build. Environ. 46:1094–103 [Google Scholar]
  53. Kaminski E, Tait S, Carazzo G. 2005. Turbulent entrainment in jets with arbitrary buoyancy. J. Fluid Mech. 526:361–76 [Google Scholar]
  54. Kaye NB, Hunt GR. 2006. Weak fountains. J. Fluid Mech. 558:319–28 [Google Scholar]
  55. Kaye NB, Hunt GR. 2007. Overturning in a filling box. J. Fluid Mech. 576:297–323 [Google Scholar]
  56. Koh RCY, Brooks NH. 1975. Fluid mechanics of waste-water disposal in the ocean. Annu. Rev. Fluid Mech. 7:187–211 [Google Scholar]
  57. Kumagai M. 1984. Turbulent buoyant convection from a source in a confined two-layered region. J. Fluid Mech. 147:105–31 [Google Scholar]
  58. Lemckert CJ. 2004. Spreading radius of fountains after impinging on a free surface. Proc. 15th Australas. Fluid Mech. Conf. M Behnia, W Lin, GD McBain Sydney: Univ. Sydney [Google Scholar]
  59. Lin W, Armfield SW. 2000a. Direct simulation of weak axisymmetric fountains in a homogeneous fluid. J. Fluid Mech. 403:67–88 [Google Scholar]
  60. Lin WE, Armfield SW. 2000b. Very weak fountains in a homogeneous fluid. Numer. Heat Transf. A 38:377–96 [Google Scholar]
  61. Lin W, Armfield SW. 2003. The Reynolds and Prandtl number dependence of weak fountains. Comput. Mech. 31:379–89 [Google Scholar]
  62. Lin W, Armfield SW. 2008. Onset of entrainment in transitional round fountains. Int. J. Heat Mass Transf. 51:5226–37 [Google Scholar]
  63. Lin YJP, Linden PF. 2005a. The entrainment due to a turbulent fountain at a density interface. J. Fluid Mech. 542:25–52 [Google Scholar]
  64. Lin YJP, Linden PF. 2005b. A model for an under floor air distribution system. Energy Build. 37:399–409 [Google Scholar]
  65. Linden PF. 1999. The fluid mechanics of natural ventilation. Annu. Rev. Fluid Mech. 31:201–38 [Google Scholar]
  66. Lynch PM, Hunt GR. 2011. The night purging of a two-storey atrium building. Build. Environ. 46:144–55 [Google Scholar]
  67. Marugán-Cruz C, Rodríguez-Rodríguez J, Martínez-Bazán C. 2009. Negatively buoyant starting jets. Phys. Fluids 21:117101 [Google Scholar]
  68. McDougall TJ. 1981. Negatively buoyant vertical jets. Tellus 33:313–20 [Google Scholar]
  69. McMillan G. 2005. Is electric arc welding linked to manganism or Parkinson's disease?. Toxicol. Rev. 24:237–57 [Google Scholar]
  70. Mehaddi R, Vauquelin O, Candelier F. 2012. Analytical solutions for turbulent Boussinesq fountains in a linearly stratified environment. J. Fluid Mech. 691:487–97 [Google Scholar]
  71. Mizushina T, Ogino F, Takeuchi H, Ikawa H. 1982. An experimental study of vertical turbulent jet with negative buoyancy. Wärme Stoffübertrag. 16:15–21 [Google Scholar]
  72. Morton BR. 1959. Forced plumes. J. Fluid Mech. 5:151–63 [Google Scholar]
  73. Morton BR. 1962. Coaxial turbulent jets. Int. J. Heat Mass Transf. 5:955–65 [Google Scholar]
  74. Morton BR, Middleton J. 1973. Scale diagrams for forced plumes. J. Fluid Mech. 58:165–76 [Google Scholar]
  75. Morton BR, Taylor G, Turner JS. 1956. Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234:1–23 [Google Scholar]
  76. Myrtroeen OJ, Hunt GR. 2010. Negatively buoyant projectiles: from weak fountains to heavy vortices. J. Fluid Mech. 657:227–37 [Google Scholar]
  77. Myrtroeen OJ, Hunt GR. 2012. On the transition from finite-volume negatively buoyant releases to continuous fountains. J. Fluid Mech. 698:168–84 [Google Scholar]
  78. Nagai T, Yamazaki H, Nagashima H, Kantha LH. 2005. Field and numerical study of entrainment laws for surface mixed layer. Deep Sea Res. II 52:1109–32 [Google Scholar]
  79. Pantzlaff L, Lueptow RM. 1999. Transient positively and negatively buoyant turbulent round jets. Exp. Fluids 27:117–25 [Google Scholar]
  80. Papanicolaou PN, Kokkalis TJ. 2008. Vertical buoyancy preserving and non-preserving fountains, in a homogeneous calm ambient. Int. J. Heat Mass Transf. 51:4109–20 [Google Scholar]
  81. Philippe P, Raufaste C, Kurowski P, Petitjeans P. 2005. Penetration of a negatively buoyant jet in a miscible liquid. Phys. Fluids 17:053601 [Google Scholar]
  82. Pottebaum TS, Gharib M. 2004. The pinch-off process in a starting buoyant plume. Exp. Fluids 37:87–94 [Google Scholar]
  83. Ricou FP, Spalding DB. 1961. Measurements of entrainment by axisymmetrical turbulent jets. J. Fluid Mech. 11:21–32 [Google Scholar]
  84. Roberts PJW, Ferrier A, Daviero G. 1997. Mixing in inclined dense jets. J. Hydraul. Eng. 123:693–99 [Google Scholar]
  85. Roberts PJW, Toms G. 1987. Inclined dense jets in flowing current. J. Hydraul. Eng. 113:323–40 [Google Scholar]
  86. Rooney GG, Linden PF. 1996. Similarity considerations for non-Boussinesq plumes in an unstratified environment. J. Fluid Mech. 318:237–50 [Google Scholar]
  87. Satti RP, Agrawal AK. 2008. Computational study of buoyancy effects in a laminar starting jet. Int. J. Heat Fluid Flow 29:527–39 [Google Scholar]
  88. Seban RA, Behnia MM, Abreu KE. 1978. Temperatures in a heated air jet discharged downward. Int. J. Heat Mass Transf. 21:1453–58 [Google Scholar]
  89. Shapiro MA. 1980. Turbulent mixing within tropopause folds as a mechanism for the exchange of chemical constituents between the stratosphere and troposphere. J. Atmos. Sci. 37:994–1004 [Google Scholar]
  90. Shrinivas AB, Hunt GR. 2014. Unconfined turbulent entrainment across density interfaces. J. Fluid Mech. 757573–98
  91. Sutherland BR, Lee B, Ansong JK. 2012. Light attenuation experiments on double diffusive plumes and fountains. Phys. Fluids 24:066605 [Google Scholar]
  92. Thorpe SA. 2005. The Turbulent Ocean Cambridge, UK: Cambridge Univ. Press
  93. Turner JS. 1966. Jets and plumes with negative or reversing buoyancy. J. Fluid Mech. 26:779–92 [Google Scholar]
  94. van den Bremer TS, Hunt GR. 2010. Universal solutions for Boussinesq and non-Boussinesq plumes. J. Fluid Mech. 644:165–92 [Google Scholar]
  95. van den Bremer TS, Hunt GR. 2014. Two-dimensional planar plumes and fountains. J. Fluid Mech. 750:210–44 [Google Scholar]
  96. Van Dyke M. 1982. An Album of Fluid Motion Stanford, CA: Parabolic
  97. Wang RQ, Law AWK, Adams EE, Fringer OB. 2009. Buoyant formation number of a starting buoyant jet. Phys. Fluids 21:125104 [Google Scholar]
  98. Wang RQ, Law AWK, Adams EE. 2011. Pinch-off and formation number of negatively buoyant jets. Phys. Fluids 23:52101 [Google Scholar]
  99. Williamson N, Armfield SW, Lin W. 2010. Transition behaviour of weak turbulent fountains. J. Fluid Mech. 655:306–26 [Google Scholar]
  100. Williamson N, Armfield SW, Lin W. 2011. Forced turbulent fountain flow behaviour. J. Fluid Mech. 671:535–58 [Google Scholar]
  101. Williamson N, Srinarayana N, Armfield SW, McBain GD, Lin W. 2008. Low-Reynolds-number fountain behaviour. J. Fluid Mech. 608:297–317 [Google Scholar]
  102. Zel'dovich YB. 1992 (1937). The asymptotic laws of freely-ascending convective flows. Selected Works of Yakov Borisovich Zel'dovich 1 Chemical Physics and Hydrodynamics JP Ostriker, GI Barenblatt, RA Sunyaev 82–85 Princeton, NJ: Princeton Univ. Press [Google Scholar]
  103. Zhang H, Baddour RE. 1997. Maximum vertical penetration of plane turbulent negatively buoyant jets. J. Eng. Mech. 123:973–77 [Google Scholar]
  104. Zhang H, Baddour RE. 1998. Maximum penetration of vertical round dense jets at small and large Froude numbers. J. Hydraul. Eng. 124:550–53 [Google Scholar]
/content/journals/10.1146/annurev-fluid-010313-141311
Loading
/content/journals/10.1146/annurev-fluid-010313-141311
Loading

Data & Media loading...

Supplemental Material

Supplementary Data

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error