A model is proposed for estimating how fire whirls may begin to move along line fires and the velocities at which they may propagate steadily against the direction of the prevailing wind, instead of moving downwind, as most moving fire whirls do. The analysis is based on theoretical considerations of two-dimensional, inviscid, piecewise-irrotational flow containing a vortex line and vortex sheets. Comparisons of the predictions with available experimental results seem to be qualitatively consistent, but theoretical questions are identified that motivate further considerations.