  Coriolis-centrifugal convection (C$^3$) in a cylindrical domain constitutes
an idealised model of tornadic storms, where the rotating cylinder represents
the mesocyclone of a supercell thunderstorm. We present a suite of C$^3$ direct
numerical simulations, analysing the influence of centrifugal buoyancy on the
formation of tornado-like vortices (TLVs). TLVs are self-consistently generated
provided the flow is within the quasi-cyclostrophic (QC) regime. This requires
the Froude number to be greater than the radius-to-height aspect ratio, $Fr
\gtrsim \gamma$. We show that the TLVs share many features with realistic
tornadoes, such as azimuthal velocity profiles, intensification of the vortex
strength, and helicity characteristics. Further, we analyse the influence of
the mechanical bottom boundary conditions on the formation of TLVs, finding
that a rotating fluid column above a stationary surface does not generate TLVs
if centrifugal buoyancy is absent. In contrast, TLVs are generated in the QC
regime with any bottom boundary conditions when centrifugal buoyancy is
present.
  Our simulations bring forth insights into natural supercell thunderstorm
systems by identifying properties that determine whether a mesocyclone becomes
tornadic or remains non-tornadic. Our $Fr \gtrsim \gamma$ predictions
dimensionally imply a critical mesocyclone angular rotation rate of
$\widetilde{\Omega}_{mc} \gtrsim \sqrt{g/H_{mc}}$. Taking a typical mesocyclone
height of $H_{mc}\approx 12$ km, this translates to
$\widetilde{\Omega}_{mc}\gtrsim 3~\times~10^{-2}$s$^{-1}$ for centrifugal
buoyancy-dominated, quasi-cyclostrophic tornadogenesis. The formation of the
simulated TLVs happens at all heights on the centrifugal buoyancy time scale
$\tau_{cb}$. This implies a roughly 1 minute, height-invariant formation for
natural tornadoes, consistent with recent observational estimates.
