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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    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.


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    LETCHFORD, NICHOLAS A. FORBES, LAWRENCE K. and HOCKING, GRAEME C. 2012. INVISCID AND VISCOUS MODELS OF AXISYMMETRIC FLUID JETS OR PLUMES. The ANZIAM Journal, Vol. 53, Issue. 03, p. 228.


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  • 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: http://dx.doi.org/10.1017/S002211200900740X
  • Published online: 10 September 2009
Abstract

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.

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Email address for correspondence: matthew.scase@nottingham.ac.uk
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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.



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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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