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The temporal evolution of the fluid circulation generated by a buoyancy forcewhen two-dimensional (2D) arrays of 2D thermals are released into a quiescentincompressible fluid is studied through the results of numerous latticeBoltzmann simulations. It is observed that the circulation magnitude grows to amaximum value in a finite time. When both the maximum circulation and the timeat which it occurs are non-dimensionalised by appropriately definedcharacteristic scales, it is shown that two simple Prandtl number (Pr)dependent scaling relations can be devised that fit these data very well overnine decades of Pr spanning the viscous and diffusive regimes and six decadesof Rayleigh number (Ra) in the low Ra regime. Also, obtained analytically isthe exact result that circulation magnitude continues to grow in time for asingle buoyant vortex ring in an infinite unbounded fluid.Comment: 4 pages, 3 figures, submitted to Physical Review Letter

Scaling of circulation in buoyancy generated vortices