Quasi-Lagrangian Models of Nascent Thermals

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Abstract
Thermals are modeled by considering their boundaries as self-advecting vortex sheets. Both slab-symmetric and axisymmetiic geometries are considered. Discussion is restricted to the case of a neutral environment, and turbulent processes are not considered. For thermals of circular cross section, the initial accelerations are obtained analytically. A numerical method is developed to simulate the evolution of thermals by time-marching. The vortex sheet is divided into finite segments, whose positions are tracked in a quasi-Lagrangian fashion. Self-advection is considered. A redistribution procedure is adopted to prevent the segments from bunching unmanageably. The induced field of motion is fully determined both inside and outside the thermal. Results show that the axisymmetric thermal rises more quickly than the slab-symmetric thermal, that both thermals develop concave bases, that vorticity maxima occur both within the concavities and on the trailing edges, and that the leading edges are remarkably smooth.

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