Global properties of a simple axisymmetric simulation of tornadogenesis

I will present the evolution of global quantities in a simple numerical axisymmetric simulation of tornadogenesis. The simulation is the one reported by me at the 20th Conference on Severe Local Storms in 2000. The domain is closed and the flow is homogeneous with constant eddy viscosity. No-slip boundary conditions are applied to the toroidal motion and free-slip ones to the meridional (radial-vertical) motion. These boundary conditions permit the initial condition to be a Beltrami flow. The initial (closed) meridional circulation has an updraft maximum on the axis and a maximum compensating downdraft at the rim. The initial toroidal circulation is counterclockwise with maximum tangential velocity near the edge of the updraft and cyclonic (anticyclonic) vorticity in the updraft (downdraft) region. If left unperturbed, the flow undergoes a slow viscous decay with no change in pattern. The flow is perturbed by introducing density anomalies (“hydrometeors”) at the top boundary above the updraft. These fall around the updraft in a concentric “rain curtain”. The hydrometeor-drag forces accelerate air with high angular momentum toward the ground. Some of this high-angular-momentum air flows out of the curtain along the ground towards the axis where it is stretched vertically, and spins up into a tornado-like vortex, which later fills from above and decays.

The model uses Arakawa's finite-difference Jacobian to prevent the false generation of global kinetic energy and angular momentum by the nonlinear advection terms, and outputs balanced global budgets of zonal and meridional kinetic energy, helicity, enstrophy, angular momentum, water, and toroidal circulation.

The most noteworthy precursor of tornado formation is a dramatic decline in vertical kinetic energy despite a conversion of potential energy into vertical kinetic energy. This decline is accompanied by rapid intensification of the global maxima in vertical, inflow and tangential velocity and pressure deficit, as the updraft maximum and pressure minimum relocates along the axis from mid to low level, and the tangential-velocity maximum moves inward and shifts from mid to low altitude.