Tornadic Descent

A theoretical model of a prototornado is constructed with a steady 2 D (x, y plane, extruded in z) potential primary flow consisting of uniform horizontal background flow plus a vortex (circulation) plus a doublet. Particle pathlines and timelines were found using a Lagrangian coordinate expansion. Secondary flow is added which begins far upstream as weak shear flow i.e., a horizontal velocity which is linearly increasing with altitude. Far upstream the shear can be expressed as y component vorticity. This bulk vorticity can be approximated by a series of vorticity sheets. The composite flow is assumed to be 2 D in the Shames-Corrsin sense, which allows z component velocity as long as it does not vary with z. The model begins after the buoyant flow of air from near the ground reaches the mesolayer. The descent requires only the bulk horizontal vorticity of the atmospheric shear and its interaction with the primary flow. Yet the descent magnitude for fluid enclosed by the outside stagnation streamline is approximately 7 times the relative wind speed at altitude. Finally, a graphical demonstration will show how horizontal sheets of horizontal vorticity become vertical sheets of horizontal vorticity in the neighborhood of the outside stagnation streamline.