An analytical model of two-cell tornadoes with emphasis on sharpness parameter affecting updrafts and a discussion on debris trajectory in outer cell

Abstract

The present model on two-cell tornadoes generalizes the one-cell model of Baker and Sterling (2017) by introducing a sharpness parameter. However, we model only the outer cell. The idea was derived from Vatistas et al. (1991) model which showed that larger values of the sharpness parameter increase the sharpness of azimuthal velocity near the periphery of maximum azimuthal velocity. This generalization brings about the cherished change, which helps better fit to tornado motion. Natural tornadoes can fit different values of the sharpness parameter, indicating the limitations of Baker and Sterling’s model. The fluid is considered Newtonian, incompressible, and non-viscous while the motion is steady. Major changes concerning the sharpness parameter are observed in the axial velocity component which behaves differently for one-cell and two-cell tornadoes in two cases, i.e., parameter less than one and parameter greater than or equal to one. A remarkable observation is that the strongest updraft shifts towards the periphery of the maximum radial velocity. Moreover, the radial profile of pressure difference at the reference height behaves quite differently for two-cell tornadoes. Furthermore, sharpness parameter affects the distance traveled by flying debris and the time taken by falling debris to reach the ground.