Abstract
A mathematical analysis of a vortex that forms about a line heat source in a region with a given constant circulation far from the heat source and the ground is presented. The regions near the centerline of the vortex and near the ground, called the core and ground regione respectively, are treated separately using boundary-layer approximations. The presence of the ground induces a strong secondary flow toward the center of the vortex near the ground. The two regions are joined by matching boundary conditions through an intermediate inviscid region far from both the vortex centerline and the ground, and by matching the volume flow rates inward near the ground boundary layer and upward in the core region. The ground boundary layer has a strong effect on the core region flow. The effect appears to increase as viscosity decreases. The results are used to estimate the intensity of the energy source necessary to provide enough energy to drive a tornado. The results should also be useful in analyzing such phenomena as fire-whirls and electrically driven laboratory vortices.
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