APPEARANCE OF A SOURCE/SINK LINE INTO A SWIRLING VORTEX
Several mathematical models applied to tornadoes consist of exact and axisymmetric solutions of the steady and incompressible Navier–Stokes equations. These models studied by Serrin,9 Goldshtik and Shtern8 describe families of fluid motions vanishing at the ground and are restricted not to develop a source nor a sink near the vortex line. Therefore, Serrin showed that the flow patterns of the resulting velocity field may have some realistic characteristics to model the mature phase of the lifetime of a tornado, in comparison with atmospheric observations. On the other hand, no reason has been given to motivate the restriction of the absence of a source/sink vortex line. Therefore, we present here the construction and the analysis of a fluid motion driven by the vertical shear near the ground, the rate of the azimuthal rotation and by the intensity of a central source/sink line. We prove the local existence and uniqueness of a family of fluid motions, leading to the genesis of such source/sink lines inside a non-rotating updraft which does not develop, before perturbation, a source nor a sink.