On the dynamics of 3-D single thermal plumes at various Prandtl numbers and Rayleigh numbers

Alain P. Vincent, David A. Yuen, David Munger, Guizhi Zhu

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Three-dimensional (3-D) numerical simulations of single turbulent thermal plumes in the Boussinesq approximation are used to understand more deeply the interaction of a plume with itself and its environment. In order to do so, we varied the Rayleigh and Prandtl numbers from Ra ~ 10 5 to Ra ~ 10 8 and from Pr ~ 0.025 to Pr ~ 70. We found that thermal dissipation takes place mostly on the border of the plume. Moreover, the rate of energy dissipation per unit mass ε T has a critical point around Pr ~ 0.7. The reason is that at Pr greater than ~0.7, buoyancy dominates inertia and thermal advection dominates wave formation whereas this trend is reversed at Pr less than ~0.7. We also found that for large enough Prandtl number (Pr ~ 70), the velocity field is mostly poloidal although this result was known for Rayleigh-Bénard convection (see Schmalzl et al. [On the validity of two-dimensional numerical approaches to time-dependent thermal convection. Europhys. Lett. 2004, 67, 390-396]). On the other hand, at small Prandtl numbers, the plume has a large helicity at large scale and a non-negligible toroidal part. Finally, as observed recently in details in weakly compressible turbulent thermal plume at Pr = 0.7 (see Plourde et al. [Direct numerical simulations of a rapidly expanding thermal plume: structure and entrainment interaction. J. Fluid Mech. 2008, 604, 99-123]), we also noticed a two-time cycle in which there is entrainment of some of the external fluid to the plume, this process being most pronounced at the base of the plume. We explain this as a consequence of calculated Richardson number being unity at Pr = 0.7 when buoyancy balance inertia.

Original languageEnglish (US)
Pages (from-to)138-156
Number of pages19
JournalGeophysical and Astrophysical Fluid Dynamics
Issue number2
StatePublished - Apr 2012

Bibliographical note

Funding Information:
Computations have been done at Réseau Québécois de Calcul Haute Performance RQCHP Montréal Québec. A.P. Vincent has an NSERC Individual Research Grant. D.A. Yuen acknowledged support from the Mathematics-Geophysics program of the National Science Foundation. We also thank Cathy Hier-Majumder for her initial efforts in this project. We also thank Ulli Hansen for discussions on infinite Prandtl convection and Jacques Richer from RQCHP for his help with code optimization. Finally, we thank the referees for their questions and suggestions.


  • 3-D turbulent thermal plumes
  • Boussinesq approximation
  • Toroidal-poloidal decomposition

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