On the Effective Buoyancy of Turbulent Thermals

An isolated, buoyant fluid parcel (or thermal) does not accelerate with its Archimedean buoyancy, because of environmental inertia (i.e. virtual mass effects). This reduces its acceleration to an `effective buoyancy’.  Here we utilize a novel correspondence with magnetostatics to derive the first complete, exact analytical expressions for effective buoyancy, for the case of ellipsoidal thermals. Such a geometry is exhibited by real, turbulent thermals in the laboratory (e.g. Scorer 1957) as well as turbulent thermals that we simulate with direct numerical simulation.  The average effective buoyancy of these turbulent thermals is  accurately captured by our analytical expressions.