Axisymmetric tornado simulations using semi-slip boundary conditions

The fluid dynamics of tornadoes is often investigated using idealized axisymmetric simulations, isolating supercell features relevant to tornadogenesis. The vortices produced by these simulations are potential vortices, characterized by a region of constant angular momentum Γ. No-slip lower boundary conditions are usually employed in numerical simulations, leading to the formation of a potential vortex boundary layer, with a two-tiered structure and a radially inward flow towards the center of the vortex (inflow). The purpose of this study is to investigate the effects of semi-slip boundary conditions on simulated tornadoes, performing idealized axisymmetric simulations. The governing parameters are a swirl ratio Sr (related to the system’s rotation) and a Reynolds number Re (related to diffusion). The semi-slip conditions are obtained by imposing a surface drag, allowing the introduction of a friction coefficient parameter (Cd), providing conditions more realistic than the no-slip and free-slip conditions usually employed in numerical simulations. The motivation for this work is that the structure of natural tornadoes is sensitive to the lower boundary conditions for friction, hence the importance of more realistic conditions. The results show that the potential vortex boundary layer is preserved for semi-slip conditions under a wide range of Cd values (Cd=0.2 − 0.005). A decrease in Cd causes a narrowing of the lower frictional tier of the boundary layer, which vanishes between Cd=0.005 and 0.001. The decrease in Cd for fixed Sr and Re results in the same changes in the vortex’s structure previously observed for no-slip simulations under increasing Sr and fixed Re. This shows that the governing parameter space is three-dimensional (Cd−Sr−Re). Finally, within the range Cd=0.2 − 0.035, a decrease in friction can lead to a vortex intensification due to the enhancement and shift of the inflow towards the vortex’s center, combined with the reduced dissipation of Γ.