  This work investigates intensive vortices, which are characterised by the
existence of a converging radial flow that significantly intensifies the flow
rotation. Evolution and amplification of the vorticity present in the flow play
important roles in the formation of the vortex. When rotation in the flow
becomes sufficiently strong - and this implies validity of the strong swirl
approximation developed by Einstein and Li (1951), Lewellen (1962), Turner
(1966) and Lundgren (1985) - the analysis of Klimenko (2001a-c) and of the
present work determine that further amplification of vorticity is moderated by
interactions of vorticity and velocity. This imposes physical constraints on
the flow resulting in the so-called compensating regime, where the radial
distribution of the axial vorticity is characterised by the 4/3 and 3/2 power
laws. This asymptotic treatment of a strong swirl is based on vorticity
equations and involves higher order terms. This treatment incorporates
multiscale analysis indicating downstream relaxation of the flow to the
compensating regime. The present work also investigates and takes into account
viscous and transient effects. One of the main points of this work is the
applicability of the power laws of the compensating regime to intermediate
regions in large atmospheric vortices, such as tropical cyclones and tornadoes.
