Coriolis-centrifugal convection (${\mathrm{C}}^3$) 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 ${\mathrm{C}}^3$ 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 in which the dominant dynamical balance is between pressure gradient and centrifugal buoyancy forces. This requires the Froude number to be greater than the radius-to-height aspect ratio, $Fr⪆\gamma$. We show that the TLVs that develop in our ${\mathrm{C}}^3$ simulations share many similar 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. For tornadoes to exist, a vertical temperature difference must be present that is capable of driving strong convection. Additionally, our $Fr⪆\gamma$ predictions dimensionally imply a critical mesocyclone angular rotation rate of ${\tilde{\mathrm{\Omega }}}_{\mathrm{m}\mathrm{c}}⪆\sqrt{g/H_{\mathrm{m}\mathrm{c}}}$. Taking a typical mesocyclone height of $H_{\mathrm{m}\mathrm{c}}\approx 12\mathrm{k}\mathrm{m}$, this translates to ${\tilde{\mathrm{\Omega }}}_{\mathrm{m}\mathrm{c}}⪆3\times {10}^{-2}{\mathrm{s}}^{-1}$ 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.

科里奥利离心对流（${\mathrm{C}}^3$）在圆柱域中构成理想的暴风雨模型，其中旋转的圆柱体代表超级单体雷暴的中旋流器。我们提出了一套${\mathrm{C}}^3$直接数值模拟，分析离心浮力对龙卷风状旋涡（TLV）形成的影响。TLV是自洽生成的，前提是流量在准环转（QC）范围内，其中主要的动态平衡在压力梯度和离心浮力之间。这要求Froude数必须大于半径与高度的长宽比，$F\mathrm{[R}⪆\gamma$。我们证明了在我们内部发展的TLV${\mathrm{C}}^3$模拟与现实龙卷风具有许多相似的特征，例如方位角速度剖面，涡旋强度的增强和螺旋度特性。此外，我们分析了机械底部边界条件对TLV形成的影响，发现如果没有离心浮力，固定表面上方的旋转流体柱不会生成TLV。相反，当存在离心浮力时，在任何底部边界条件下，在QC方案中都会生成TLV。我们的模拟通过识别确定中旋流器变为隆隆型还是非隆隆型的性质，为天然超级细胞雷暴系统提供了见识。为了使龙卷风存在，必须存在能够驱动强对流的垂直温差。另外，我们的$F\mathrm{[R}⪆\gamma$ 预测在尺寸上暗示了临界的中气旋气旋角旋转速率 ${\stackrel{〜}{\mathrm{\Omega }}}_{\mathrm{米}\mathrm{C}}⪆\sqrt{G/H_{\mathrm{米}\mathrm{C}}}$。采取典型的中气旋高度$H_{\mathrm{米}\mathrm{C}}\approx 12\mathrm{ķ}\mathrm{米}$，这意味着 ${\stackrel{〜}{\mathrm{\Omega }}}_{\mathrm{米}\mathrm{C}}⪆3\times {10}^{-\mathrm{2个}}{\mathrm{s}}^{-\mathrm{1个}}$用于离心浮力为主的准环营养旋流成因。模拟TLV的形成发生在离心浮力时间尺度上的所有高度${\tau }_{Cb}$。这意味着自然龙卷风大约会在1分钟内保持高度不变，这与最近的观测估计是一致的。