  By introducing an equivalence between magnetostatics and the equations
governing buoyant motion, we derive analytical expressions for the acceleration
of isolated density anomalies, a.k.a. 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 $\textit{Re}=6300$. 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 still accurately relate the buoyant
acceleration to the thermal's mean Archimedean buoyancy and aspect ratio. Thus,
our analytical formulae provide a simple and direct means of estimating the
buoyant acceleration of turbulent thermals.
