Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 12
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Craske, John and van Reeuwijk, Maarten 2016. Generalised unsteady plume theory. Journal of Fluid Mechanics, Vol. 792, p. 1013.

    Woodhouse, M. J. Phillips, J. C. and Hogg, A. J. 2016. Unsteady turbulent buoyant plumes. Journal of Fluid Mechanics, Vol. 794, p. 595.

    Craske, John and van Reeuwijk, Maarten 2015. Energy dispersion in turbulent jets. Part 1. Direct simulation of steady and unsteady jets. Journal of Fluid Mechanics, Vol. 763, p. 500.

    Craske, John and van Reeuwijk, Maarten 2015. Energy dispersion in turbulent jets. Part 2. A robust model for unsteady jets. Journal of Fluid Mechanics, Vol. 763, p. 538.

    Carlotti, Pierre Vallerent, Stéphanie Fromy, Philippe and Demouge, François 2012. Smoke motion: comparison of experimental data with simulations. Proceedings of the Institution of Civil Engineers - Engineering and Computational Mechanics, Vol. 165, Issue. 4, p. 235.

    Hargreaves, David M. Scase, Matthew M. and Evans, Iona 2012. A simplified computational analysis of turbulent plumes and jets. Environmental Fluid Mechanics, Vol. 12, Issue. 6, p. 555.


    Scase, M. M. and Hewitt, R. E. 2012. Unsteady turbulent plume models. Journal of Fluid Mechanics, Vol. 697, p. 455.

    Alon, Gali Philip, Jimmy and Cohen, Jacob 2011. The development of a buoyant vortex in stationary and plane stagnation flows. European Journal of Mechanics - B/Fluids, Vol. 30, Issue. 3, p. 288.

    Holland, Paul R. 2011. Oscillating Dense Plumes. Journal of Physical Oceanography, Vol. 41, Issue. 8, p. 1465.

    Yamamoto, H. Cenedese, C. and Caulfield, C. P. 2011. Laboratory experiments on two coalescing axisymmetric turbulent plumes in a rotating fluid. Physics of Fluids, Vol. 23, Issue. 5, p. 056601.

    Scase, M. M. 2009. Evolution of volcanic eruption columns. Journal of Geophysical Research, Vol. 114, Issue. F4,

  • Journal of Fluid Mechanics, Volume 635
  • September 2009, pp. 137-169

The effect of sudden source buoyancy flux increases on turbulent plumes

  • M. M. SCASE (a1), A. J. ASPDEN (a2) and C. P. CAULFIELD (a3) (a4)
  • DOI:
  • Published online: 10 September 2009

Building upon the recent experimentally verified modelling of turbulent plumes which are subject to decreases in their source strength (Scase et al., J. Fluid Mech., vol. 563, 2006b, p. 443), we consider the complementary case where the plume's source strength is increased. We consider the effect of increasing the source strength of an established plume and we also compare time-dependent plume model predictions for the behaviour of a starting plume to those of Turner (J. Fluid Mech., vol. 13, 1962, p. 356).

Unlike the decreasing source strength problems considered previously, the relevant solution to the time-dependent plume equations is not a simple similarity solution. However, scaling laws are demonstrated which are shown to be applicable across a large number of orders of magnitude of source strength increase. It is shown that an established plume that is subjected to an increase in its source strength supports a self-similar ‘pulse’ structure propagating upwards. For a point source plume, in pure plume balance, subjected to an increase in the source buoyancy flux F0, the rise height of this pulse in terms of time t scales as t3/4 while the vertical extent of the pulse scales as t1/4. The volume of the pulse is shown to scale as t9/4. For plumes in pure plume balance that emanate from a distributed source it is shown that the same scaling laws apply far from the source, demonstrating an analogous convergence to pure plume balance as that which is well known in steady plumes. These scaling law predictions are compared to implicit large eddy simulations of the buoyancy increase problem and are shown to be in good agreement.

We also compare the predictions of the time-dependent model to a starting plume in the limit where the source buoyancy flux is discontinuously increased from zero. The conventional model for a starting plume is well approximated by a rising turbulent, entraining, buoyant vortex ring which is fed from below by a ‘steady’ plume. However, the time-dependent plume equations have been defined for top-hat profiles assuming only horizontal entrainment. Therefore, this system cannot model either the internal dynamics of the starting plume's head or the extra entrainment of ambient fluid into the head due to the turbulent boundary of the vortex ring-like cap. We show that the lack of entrainment of ambient fluid through the head of the starting plume means that the time-dependent plume equations overestimate the rise height of a starting plume with time. However, by modifying the entrainment coefficient appropriately, we see that realistic predictions consistent with experiment can be attained.

Corresponding author
Email address for correspondence:
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

A. S. Almgren , J. B. Bell , P. Colella , L. H. Howell & M. L. Welcome 1998 A conservative adaptive projection method for the variable density incompressible Navier–Stokes equations. J. Comp. Phys. 142, 146.

A. S. Almgren , J. B. Bell & W. Y. Crutchfield 2000 Approximate projection methods. Part I. Inviscid analysis. SIAM J. Sci. Comp. 22, 11391159.

A. J. Aspden , N. Nikiforakis , S. B. Dalziel & J. B. Bell 2008 Analysis of implicit LES methods. Comm. Appl. Math. Comput. Sci. 3, 103126.

J. P. Boris 1990 On large eddy simulation using subgrid turbulence models. Comment 1. In Lecture notes in Physics (ed. J. L. Lumley ), vol. 357, pp. 344353. Springer Verlag.

J. P. Boris , F. F. Grinstein , E. S. Oran & R. L. Kolbe 1992 New insights into large eddy simulation. Fluid Dyn. Res. 10, 199229.

C. P. Caulfield & A. W. Woods 1995 Plumes with non-monotonic mixing behaviour. Geophys. Astrophys. Fluid Dyn. 79, 173199.

P. Colella 1985 A direct Eulerian MUSCL scheme for gasdynamics. SIAM J. Sci. Stat. Comp. 6, 104117.

P. Colella 1990 A multidimensional second order Godunov scheme for conservation laws. J. Comp. Phys. 87, 171200.

D. Drikakis , C. Fuerby F. F. Grinstein & D. L. Youngs 2007 Simulation of transition and turbulence decay in the Taylor–Green vortex. J. Turbul. 8, 112.

C. Fureby & F. F. Grinstein 1999 Monotonically integrated large eddy simulations of free shear flows. AIAA J. 37, 544556.

M. J. M. Hill 1894 On a spherical vortex. Phil. Trans. R. Soc. A 185, 213245.

J. Levine 1959 Spherical vortex theory of bubble-like motion in cumulus clouds. J. Meteor. 16, 653662.

L. G. Margolin , W. J. Rider & F. F. Grinstein 2006 Modeling turbulent flow with implicit LES. J. Turbul. 7, 127.

B. R. Morton , G. I. Taylor & J. S. Turner 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234, 132.

E. S. Oran & J. P. Boris 1993 Computing turbulent shear flows – a convenient conspiracy. Comp. Phys. 7, 523533.

D. H. Porter , A. Pouquet & P. R. Woodward 1992 Three-dimensional supersonic homogeneous turbulent: a numberical study. Phys. Rev. Lett. 68, 3156.

R. S. Scorer 1954 The nature of convection as revealed by soaring birds and dragonflies. Q. J. R. Met. Soc. 80, 6877.

J. S. Turner 1957 Buoyant vortex rings. Proc. R. Soc. A 239, 6175.

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? *