  This paper investigates the steady axisymmetric structure of the cold
boundary-layer flow surrounding fire whirls developing over localized fuel
sources lying on a horizontal surface. The inviscid swirling motion found
outside the boundary layer, driven by the entrainment of the buoyant turbulent
plume of hot combustion products that develops above the fire, is described by
an irrotational solution, obtained by combining Taylor's self-similar solution
for the motion in the axial plane with the azimuthal motion induced by a line
vortex of circulation $2 \pi \Gamma$. The development of the boundary layer
from a prescribed radial location is determined by numerical integration for
different swirl levels, measured by the value of the radial-to-azimuthal
velocity ratio $\sigma$ at the initial radial location. As in the case
$\sigma=0$, treated in the seminal boundary-layer analysis of Burggraf et al.
(Phys. Fluids, 1971), the pressure gradient associated with the centripetal
acceleration of the inviscid flow is seen to generate a pronounced radial
inflow. Specific attention is given to the terminal shape of the boundary-layer
velocity near the axis, which displays a three-layered structure that is
described by matched asymptotic expansions. The resulting composite expansion,
dependent on the level of ambient swirl through the parameter $\sigma$, is
employed as boundary condition to describe the deflection of the boundary-layer
flow near the axis to form a vertical swirl jet. Numerical solutions of the
resulting non-slender collision region for different values of $\sigma$ are
presented both for inviscid flow and for viscous flow with moderately large
values of the controlling Reynolds number $\Gamma/\nu$. The velocity
description provided is useful in mathematical formulations of localized
fire-whirl flows, providing consistent boundary conditions accounting for the
ambient swirl level.
