2018/06/28 by Nathaniel Tarshish, Nadir Jeevanjee, Daniel Lecoanet
Engineering · Environmental Science · Physics and Astronomy · #Acceleration #Buoyancy #Classical mechanics #Fluid Dynamics and Turbulent Flows #Mechanics #Neutral buoyancy #Physics #Plant Water Relations and Carbon Dynamics #Reynolds number #Solar and Space Plasma Dynamics #Thermal #Thermodynamics #Turbulence #physics.ao-ph #physics.flu-dyn
paper · pdf · doi:10.1175/jas-d-17-0371.1
openalex publication_date 2018/06/28 · arxiv created 2018/09/23 · arxiv updated 2018/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.