Effect of the lower boundary condition on tornado intensity in an axisymmetric, constant-viscosity, closed model of tornadogenesis 14.5

A simple, axisymmetric, constant-viscosity model of tornadogenesis in a closed domain demonstrates how some tornadoes might form by Fujita's recycling mechanism. The initial condition consists of a Beltrami flow with a central updraft and mid-level mesocyclone, surrounded by an anticyclonic downdraft. The initial flow if left unperturbed decays slowly without changing pattern. Precipitation is introduced above the updraft through the top boundary and falls in an annular rain curtain near the updraft/downdraft interface. The associated precipitation drag forces locally enhance the downdraft. The augmented downdraft and its outflow towards the axis transport air with moderately high angular momentum (AM) downward and inward, leading to formation of a tornado at the foot of the axis.

The effect of the lower boundary condition (LBC) on the intensity of the tornado is investigated by using three different conditions, namely (i) no slip on v, the tangential wind, and free slip on u, the radial wind, (ii) free slip on both u and v, and (iii) no slip on both u and v. Condition (i) allows the strong, almost radially inward, flow next to the ground that occurs in vortices with turbulent boundary layers.

With LBC (i), an intense tornado with an axial jet forms. Measures of the near-surface intensification of this vortex relative to the tornado cyclone aloft, and the relative strengths of the maxima in the three wind components agree well with theoretical predictions and values for some numerically simulated vortices.

When LBC (ii) is used, the centrifugal force is unreduced near the ground, and, as the air spins up, is able in time to balance the inward pressure-gradient force. This balance occurs on the tornado scale, not the mesocyclone scale, so a weak short-lived tornado still forms. Its central downdraft quickly reaches the ground, and produces a two-celled vortex structure with a widening inner cell.

An end-wall vortex still forms with LBC (iii). However, it is considerably weaker than with LBC (i) because the inflow into the vortex is slower, deeper, more elevated and less radial, and the contours of AM do not descend as far. Consequently, the tornado develops slowly. It is stronger than the tornado in the free-slip case because the maximum inflow, which is located close to the ground, moves inward further and drives air with relatively high AM closer to the axis. In the simulations, the viscosity is low enough that this effect outweighs the loss of AM owing to the frictional torque.