A class of unsteady self-similar flows without an ``essential'' singularity and a mechanism of whirlwind formation (Q1317782)

A class of self-similar flows comprising more than 20 problems which can be combined in five different formulations is considered. These flows can have an ``essential'' singularity only at the initial instant of time (for example, a powerful explosion) and subsequently do not contain singularities of the energy or mass source type. Flows caused by the motion of bodies are excluded from consideration, i.e., cases in which the flow is bounded by fixed or free boundaries with zero pressure on the latter are considered. In the case of an ideal fluid vortex, singularities at which no energy is released are admitted. A class of flows corresponding to the ``self-motions'' of a fluid originating from an initial state with a singularity is considered. Plane flows and flows with spherical and axial symmetry are considered. Flows of this class describing the ascent of a vortex ring from a small initially heated region and possible generalizations are examined in detail, together with a mechanism of whirlwind formation.