Quasi-Lagrangian models of nascent thermals

Slab-symmetric and axisymmetric geometries are considered in the modeling of thermals by considering their boundaries as self-advecting vortex sheets, for the case of a neutral environment without turbulent processes. The initial accelerations for circular cross section thermals are obtained analytically, and a numerical method is developed to simulate the evolution of thermals by time-marching in which the vortex sheet is divided into finite segments whose positions are tracked in a quasi-Lagrangian fashion. Self-advection is considered, and a redistribution procedure is adopted to prevent the segments from bunching unmanageably. The induced field of motion is determined both inside and outside the thermal. It is shown that (1) the axisymmetric thermal rises more quickly than the slab-symmetric thermal, (2) vorticity maxima occur both within the concavities and on the trailing edges, and (3) the leading edges are very smooth.