On the buoyant acceleration of fluid parcels

It is well known that the acceleration of an anomalously dense fluid parcel is not fully captured by the Archimedean buoyancy B, and that the net buoyant acceleration also includes an offsetting contribution from the perturbation pressure gradient. This contribution is often ignored, however, and an analytical estimate of its size is still lacking. Here, we fill this gap by solving the relevant Poisson equation for uniform cylindrical density anomalies located both near a lower boundary and in free space. This yields analytical expressions for the net buoyant acceleration as functions of the cylinder's Archimedean buoyancy B and aspect ratio R/H, where R and H are the radius and height of the cylinder, respectively. Our expressions quantify the (often significant) difference between the net buoyant acceleration and B, and show that parcels of a given B and R/H accelerate much more slowly near a boundary than far from it. Our expressions are encouragingly accurate for more realistic, non-uniform Gaussian density distributions, and successfully predict the initial motion of cylindrical density anomalies in atmospheric Large-Eddy Simulations, which cannot be done with B alone.