Vortex sheets, vortex rings, and a mesocyclone

The simplest illustration of mesocyclone formation can be constructed from the interaction of a low-level shear zone and a convective updraft. These features can be simply represented by a collection of vortex sheets above a lower boundary and horiontal vortex ring above the shear zone. In turn, vortex sheets and vortex rings can be approximated by a collection of lines, each of which are described by a series of connected points which trace vortex lines in the fluid.

The evolution of three-dimensional, incompressible, inviscid fluid flow can in fact be computed in exactly this manner, by what is referred to as "three-dimensional vortex methods." Each vortex line, represented by a chain of vortex segments, induces a motion field on itself and all the other vortex lines through the usual inversion of the velocity field from the vorticity using the Biot-Savart kernel.

Using these methods, we explore how vertical vorticity and velocity are generated by the tilting of horizontal vortex lines into the vertical by convection. For example, the preferential development of stronger cyclonic vorticity on the right side of the updraft is found when the low-level shear turns to the right with height.