An asymptotic expansion of the Navier—Stokes equations is proposed which provides a new basis for previously stated free‐vortex equations. Two main parameters emerge from the description of vortex generation. One is a conventional Ekman number, and the other indicates that unless the product of the area of the updraft and the average vertical gradient of the vertical velocity greatly exceeds the kinematic viscosity coefficient, no localized vortical flow develops. Although the model is largely axially invariant, the isobars described by the model are easily shown to have a funnel‐cloud‐like shape. Finally it is proposed that the analysis (although laminar) may suggest the counterforces basic to the generation of concentrated geophysical vortices: a vertical updraft induces a radial inflow, which may concentrate ambient angular momentum into a vortex unless turbulent viscous forces counteract the intensification.