Skip to main content Accessibility help

The evolution of laminar thermals

  • J. W. Atkinson (a1) and P. A. Davidson (a1)


We consider the life cycle of an axisymmetric laminar thermal starting from the initial condition of a Gaussian buoyant blob. We find that, as time progresses, the thermal transitions through a number of distinct stages, undergoing several morphological changes before ending up as a vortex ring. Whilst each stage is interesting in its own right, one objective of this study is to set out a consistent mathematical framework under which the entire life cycle can be studied. This allows examination of the transition between the different stages, as well as shedding light on some unsolved questions from previous works. We find that the early stages of formation are key in determining the properties of the final buoyant vortex ring and that, since they occur on a time scale where viscosity has little effect, the final properties of the ring display an independence above a critical Reynolds number. We also find that rings consistently contain the same proportion of the initial heat and have a consistent vorticity flux. By considering the effect of Prandtl number, we show that thermal diffusion can have a significant impact on development, smoothing out the temperature field and inhibiting the generation of vorticity. Finally, by considering the wake left behind as well as the vortex ring that is generated, we observe that the wake can itself roll up to form a second mushroom cap and subsequently a secondary vortex ring that follows the first.


Corresponding author

Email address for correspondence:


Hide All
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Davidson, P. A., Sreenivasan, B. & Aspden, A. J. 2007 Evolution of localized blobs of swirling or buoyant fluid with and without an ambient magnetic field. Phys. Rev. E 75 (2), 026304.
Gharib, M., Rambod, E. & Shariff, K. 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121140.
Griffiths, R. W. 1986 Thermals in extremely viscous fluids, including the effects of temperature-dependent viscosity. J. Fluid Mech. 166, 115138.
Harlow, F. H. & Welch, J. E. 1965 Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8 (12), 2182.
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Saffman, P. G. 1970 The velocity of viscous vortex rings. Stud. Appl. Maths 49 (4), 371380.
Saffman, P. G. 1992 Vortex Dynamics. Cambridge University Press.
Sànchez, O., Raymond, D. J., Libersky, L. & Petschek, A. G. 1989 The development of thermals from rest. J. Atmos. Sci. 46 (14), 22802292.
Scorer, R. S. 1957 Experiments on convection of isolated masses of buoyant fluid. J. Fluid Mech. 2 (06), 583594.
Scorer, R. S. 1978 Environmental Aerodynamics. Halsted.
Shlien, D. J. 1976 Some laminar thermal and plume experiments. Phys. Fluids 19 (8), 10891098.
Shlien, D. J. & Thompson, D. W. 1975 Some experiments on the motion of an isolated laminar thermal. J. Fluid Mech. 72 (01), 3547.
Thompson, D. W. 1961 On Growth and Form. Cambridge University Press.
Turner, J. S. 1957 Buoyant vortex rings. Proc. R. Soc. Lond. A 239 (1216), 6175.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Related content

Powered by UNSILO

The evolution of laminar thermals

  • J. W. Atkinson (a1) and P. A. Davidson (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.