Large -eddy simulation of a three-dimensional compressible tornado vortex

Large-Eddy simulation (LES) has become a very useful tool for investigating tornadoes, one of the more spectacular and destructive phenomena of nature. A new three-dimensional, unsteady, compressible model is generated to determine how significant the differences between compressible and incompressible LES simulations may be in some extremely violent tornadoes. In particular, this study seeks to determine how high the Mach number within the tornado may become before significant changes occur due to compressibility, and what the major effects of these changes may be expected to be.;After developing and verifying the compressible LES model, three different patterns of tornadic corner flows cataloged by local swirl ratio are simulated under quasisteady conditions for different Mach numbers. Simulation comparisons have demonstrated that the compressibility effects are different for different corner flow structures. At peak average Mach numbers less than approximately 0.5, the compressibility effects are not very significant and may be accounted for to leading order by an appropriate isentropic transformation applied to the incompressible results. As the maximum Mach number is increased to more than 1.0, the compressibility effects for low-swirl-ratio corner flows are dramatic, with significant increase in peak vertical velocity and the height of the vortex breakdown above the surface. The effects are much weaker for medium swirl conditions, and expected to be still weaker for high swirl corner flow where the effects are essentially limited to influencing the secondary vortices. In general, compressibility effects would not change the basic dynamics of tornadic corner flows even if Mach numbers greater than one are achieved.;This study also shows that during the sharp temporal overshoot in near-surface intensity that can sometimes occur during a tornado\u27s evolution, the maximum pressure drop will tend to be restricted by supersonic velocities, and thus limit the intensification of the overshoot. There are no apparent physical barriers to transonic speeds occurring within real tornadoes on rare occasions, however it is believed that most tornado dynamics are not significantly impacted by Mach number effects. There may be occasions when the maximum velocity within a tornado is limited by sonic conditions for brief periods but it is a soft limit which allows modest supersonic velocities that would be difficult to observe in an actual tornado