The initial transient and approach to self-similarity of a very viscous buoyant thermal

An isolated buoyant thermal in very viscous fluid has been shown to attain a self-similar form at large times which grows as t^{1/2}(Whittaker & Lister J. Fluid Mech. , vol. 606, 2008, pp. 295–324). For large values of the Rayleigh number \mathit{Ra}(based on the conserved total buoyancy), the similarity solution is slender with a roughly spherical head at the top and a long tail that contains most of the buoyancy and extends down to...