Environmental Fluid Mechanics

, Volume 12, Issue 4, pp 347–359 | Cite as

The flow of high-Reynolds axisymmetric gravity currents of a stratified fluid into a stratified ambient: shallow-water and box model solutions

  • T. Zemach
  • M. Ungarish
Original Article


We consider the axisymmetric flow (in a full cylinder or a wedge) of high-Reynolds-number Boussinesq gravity currents and intrusions systems in which both the ambient and the propagating “current” are linearly stratified. The main focus is on a current of fixed volume released from a cylinder lock; the height ratio of the fluids H, and the stratification parameter of the ambient S, are quite general. We develop a one-layer shallow-water model. The internal stratification enters as a new dimensionless parameter, \({\sigma \in [0, 1]}\). In general, the time-dependent motion is obtained by standard finite-difference solutions; a self-similar analytical solution exists for S = 0. We show that, in general, the speed of propagation decreases when the internal stratification becomes more pronounced (σ increases). We also developed a box-model approximation, and show that the resulting radius of propagation is in good agreement with the more rigorous shallow-water prediction.


Gravity current Axisymmetric flow Stratified Shallow-water 


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  1. 1.
    Benjamin T (1968) Gravity currents and related phenomena. J Fluid Mech 31: 209–248CrossRefGoogle Scholar
  2. 2.
    Bonnecaze RT, Huppert HE, Lister JR (1993) Particle-driven gravity currents. J Fluid Mech 250: 339–369CrossRefGoogle Scholar
  3. 3.
    Hoyler J, Huppert H (1980) Gravity currents entering a two-layer fluid. J Fluid Mech 100: 739–767CrossRefGoogle Scholar
  4. 4.
    Huppert H, Simpson J (1980) The slumping of gravity currents. J Fluid Mech 99: 785–799CrossRefGoogle Scholar
  5. 5.
    Maurer BD, Bolster DT, Linden PF (2010) Intrusive gravity currents between two stably stratified fluids. J Fluid Mech 647: 53–69CrossRefGoogle Scholar
  6. 6.
    Morton KW, Mayers DF (1998) Numerical solution of PDE. Cambridge university press, CambridgeGoogle Scholar
  7. 7.
    Rottman J, Simpson J (1983) Gravity currents produced by instantaneous release of a heavy fluid in a rectangular channel. J Fluid Mech 135: 95–110CrossRefGoogle Scholar
  8. 8.
    Simpson J (1997) Gravity currents in the environment and the laboratory. Cambridge University Press, CambridgeGoogle Scholar
  9. 9.
    Ungarish M (2009) An Introduction to gravity currents and intrusions. CRC Press, Boca RatonCrossRefGoogle Scholar
  10. 10.
    Ungarish M (2011) Gravity current and intrusions of stratified fluids into a stratified ambient. Environ Fluid Mech. doi: 10.1007/s10652-011-9216-1
  11. 11.
    Ungarish M, Huppert H (2002) On gravity currents propagating at the base of a stratified ambient. J Fluid Mech 458: 283–301CrossRefGoogle Scholar
  12. 12.
    Ungarish M, Huppert H (2004) On gravity currents propagating at the base of a stratified ambient:effects of geometrical constraints and rotation. J Fluid Mech 521: 69–104CrossRefGoogle Scholar
  13. 13.
    Ungarish M, Zemach T (2007) On axisymmetric intrusive gravity currents in a stratified ambient - shallow-water theory and numerical results. Eur J Mech B/Fluids 26: 220–235CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of Computer ScienceTel-Hai CollegeTel-HaiIsrael
  2. 2.Department of Computer ScienceTechnionHaifaIsrael

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