Exact solutions for unsteady axisymmetric vortex motions governing atmospheric vortices

It is concluded from the unsteady model extended from the Rankine combined model that when time tends to infinity, the core radius vanishes for inviscid flows. However, the unsteady viscous flow model, extended from the Burgers-Rott model, reveals that, when time tends to infinity, the core radius becomes infinitely large for zero axial pressure gradient but stabilises if the axial pressure gradient is non-zero. Thus, it is concluded that a vortex survives with time only when the flow is viscous and the axial pressure gradient is non-zero.