Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-26T17:12:15.822Z Has data issue: false hasContentIssue false
  • English
  • Français

The evolution of laminar thermals

Published online by Cambridge University Press:  18 September 2019

J. W. Atkinson Open the ORCID record for J. W. Atkinson [Opens in a new window]  and
P. A. Davidson Open the ORCID record for P. A. Davidson [Opens in a new window]
J. W. Atkinson*
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, CambridgeCB2 1PZ, UK
P. A. Davidson
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, CambridgeCB2 1PZ, UK
*
†Email address for correspondence: jwa34@cam.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

JFM classification

Vortex Flows: Vortex dynamics Convection: Plumes/thermals
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 878 , 10 November 2019 , pp. 907 - 931
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
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.Google Scholar
Gharib, M., Rambod, E. & Shariff, K. 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121–140.Google Scholar
Griffiths, R. W. 1986 Thermals in extremely viscous fluids, including the effects of temperature-dependent viscosity. J. Fluid Mech. 166, 115–138.Google Scholar
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.Google Scholar
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.Google Scholar
Saffman, P. G. 1970 The velocity of viscous vortex rings. Stud. Appl. Maths 49 (4), 371–380.Google Scholar
Saffman, P. G. 1992 Vortex Dynamics. Cambridge University Press.Google Scholar
Sànchez, O., Raymond, D. J., Libersky, L. & Petschek, A. G. 1989 The development of thermals from rest. J. Atmos. Sci. 46 (14), 2280–2292.Google Scholar
Scorer, R. S. 1957 Experiments on convection of isolated masses of buoyant fluid. J. Fluid Mech. 2 (06), 583–594.Google Scholar
Scorer, R. S. 1978 Environmental Aerodynamics. Halsted.Google Scholar
Shlien, D. J. 1976 Some laminar thermal and plume experiments. Phys. Fluids 19 (8), 1089–1098.Google Scholar
Shlien, D. J. & Thompson, D. W. 1975 Some experiments on the motion of an isolated laminar thermal. J. Fluid Mech. 72 (01), 35–47.Google Scholar
Thompson, D. W. 1961 On Growth and Form. Cambridge University Press.Google Scholar
Turner, J. S. 1957 Buoyant vortex rings. Proc. R. Soc. Lond. A 239 (1216), 61–75.Google Scholar