Title: Development of non-modal shear induced instabilities in atmospheric tornadoes,
Abstract: In this paper we consider the role of nonmodal instabilities in the dynamics
of atmospheric tornadoes. For this purpose we consider the Euler equation,
continuity equation and the equation of state and linearise them. As an example
we study several different velocity profiles: the so-called Rankine vortex
model; the Burgers-Rott vortex model; Sullivan and modified Sullivan vortex
models. It has been shown that in the two dimensional Rankine vortex model no
instability appears in the inner region of a tornado. On the contrary, outside
this area the physical system undergoes strong exponential instability. We have
found that initially perturbed velocity components lead to amplified sound wave
excitations. The similar results have been shown in Burgers-Rott vortex model
as well. As it was numerically estimated, in this case, the unstable wave
increases its energy by a factor of $400$ only in $\sim 0.5$min. According to
the numerical study, in Sullivan and modified Sullivan models, the instability
does not differ much by the growth. Despite the fact that in the inner area the
exponential instability does not appear in a purely two dimensional case, we
have found that in the modified Sullivan vortex even a small contribution from
vertical velocities can drive unstable nonmodal waves.