Coriolis-离心对流准旋转系中的类龙卷涡旋
Tornado-Like Vortices in the Quasi-Cyclostrophic Regime of Coriolis-Centrifugal Convection
摘要：
圆柱形区域中的科里奥利离心对流（C $^3$）构成了龙卷风风暴的理想模式，其中旋转圆柱体代表超级单体雷暴的中气旋。我们提出了一套C $^3$直接数值模拟，分析了离心浮力对龙卷风状涡（TLVs）形成的影响。TLV是自洽产生的流动是在准旋（QC）制度。这要求弗劳德数大于半径与高度的纵横比$Fr \gtrsim γ$。我们发现，TLVs共享许多功能与现实的龙卷风，如方位角速度剖面，加剧的涡旋强度，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，则静止表面上方的旋转流体柱不会产生TLV。相比之下，当存在离心浮力时，在具有任何底部边界条件的QC状态下生成TLV。我们的模拟带来了洞察自然超级单体雷暴系统，确定属性，决定是否成为龙卷风或保持非龙卷风。我们的$Fr \gtrsim γ$预测在维度上意味着一个临界中气旋角旋转速率为$\widetildeΩ_{mc} \gtrsim \sqrt{g/H_{mc}}$。以典型的中气旋高度$H_{mc}\approx 12$ km为例，对于离心浮力主导的准旋转龙卷风生成，这转化为$\widetildeΩ_{mc}\gtrsim 3~\times~10^{-2}$ s $^{-1}$。模拟TLV的形成发生在离心浮力时间尺度$τ_{cb}$上的所有高度。这意味着自然龙卷风的形成时间约为1分钟，高度不变，与最近的观测估计一致。
英文摘要：
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, $Fr \gtrsim γ$. 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 $Fr \gtrsim γ$ predictions dimensionally imply a critical mesocyclone angular rotation rate of $\widetildeΩ_{mc} \gtrsim \sqrt{g/H_{mc}}$. Taking a typical mesocyclone height of $H_{mc}\approx 12$ km, this translates to $\widetildeΩ_{mc}\gtrsim 3~\times~10^{-2}$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 $τ_{cb}$. This implies a roughly 1 minute, height-invariant formation for natural tornadoes, consistent with recent observational estimates.
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