Tornadogenesis with and without a dynamic pipe effect

A dynamic pipe effect (DPE) has been used previously to explain the descent from aloft of tornadic vortex signatures (TVSs), and presumably embryonic tornadoes, prior to the near-ground spinup of the tornado. But for many tornadoes the TVS appears to form simultaneously over a depth spanning the lowest few kilometers. A numerical model is used to determine the conditions under which a tornado is or is not preceded by a DPE. The model governs two-dimensional, axisymmetric, forced convection inside a closed, impermeable cylinder that rotates at a constant rate. Motion relative to the tank is initiated by a time-independent buoyancy field that is varied in a suite of experiments. The need for a DPE in vortex development in the model is shown to depend on trajectories of high-angular-momentum air, driven at least initially by this buoyancy field. Indeed, when buoyancy is confined primarily to midlevels, convergence at the foot of the vertical axis is weak initially, parcels with high angular momentum approach closest to the axis first at midlevels, and the vortex forms aloft (mode I). As the vortex intensifies and becomes cyclostrophically balanced, its central pressure drops and lateral motion into its core is inhibited. The resultant vertical pressure gradient and radial convergence below the vortex core increase, allowing parcels to approach the axis - and thus affording vortex spinup - at progressively lower levels. This process is the DPE. When significant buoyancy is present at low levels, air parcels that nearly conserve angular momentum are transported close to the axis over a relatively deep layer inclusive of the lower levels. The vortex in this case forms at low and midlevels at the same time, precluding a need for a DPE (mode II). A simple analytical model is used to illustrate the two modes of vortex formation, and to generalize the conclusions drawn from the numerical model. A time-dependent version of the Burgers-Rott vortex due to Rott demonstrates vortex formation without a DPE. In this exact solution of the Navier-Stokes equations, horizontal convergence and angular momentum are independent of height, and the meridional flow is steady. A simple analytical solution for the DPE has not been found. However, it can be shown qualitatively that a vortex that develops aloft, because either the large-scale convergence or the ambient angular momentum increases with height, induces below itself an axial jet and increased radial inflow at low levels.