Buoyant motion of a turbulent thermal

Nathaniel Tarshish*, Nadir Jeevanjee, Daniel Lecoanet

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

By introducing an equivalence between magnetostatics and the equations governing buoyant motion, we derive analytical expressions for the acceleration of isolated density anomalies (thermals). In particular, we investigate buoyant acceleration, defined as the sum of the Archimedean buoyancy B and an associated perturbation pressure gradient. For the case of a uniform spherical thermal, the anomaly fluid accelerates at 2B/3, extending the textbook result for the induced mass of a solid sphere to the case of a fluid sphere. For a more general ellipsoidal thermal, we show that the buoyant acceleration is a simple analytical function of the ellipsoid's aspect ratio. The relevance of these idealized uniform-density results to turbulent thermals is explored by analyzing direct numerical simulations of thermals at a Reynolds number (Re) of 6300. We find that our results fully characterize a thermal's initial motion over a distance comparable to its length. Beyond this buoyancy-dominated regime, a thermal develops an ellipsoidal vortex circulation and begins to entrain environmental fluid. Our analytical expressions do not describe the total acceleration of this mature thermal, but they still accurately relate the buoyant acceleration to the thermal's mean Archimedean buoyancy and aspect ratio. Thus, our analytical formulas provide a simple and direct means of estimating the buoyant acceleration of turbulent thermals.

Original languageEnglish (US)
Pages (from-to)3233-3244
Number of pages12
JournalJournals of the Atmospheric Sciences
Volume75
Issue number9
DOIs
StatePublished - Sep 1 2018
Externally publishedYes

Keywords

  • Buoyancy
  • Buoyancy
  • Clouds
  • Clouds
  • Convection
  • Dynamics

ASJC Scopus subject areas

  • Atmospheric Science

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