The predictions of Horn & Aurnou (2021, Journal of Turbulence 22:297–324) for tornado formation in the quasi-cyclostrophic (QC) regime of Coriolis-centrifugal convection — the tornado-like-vortex existence boundary Fr≳γFr\gtrsim\gamma (equivalently the critical mesocyclone angular rotation rate Ω~mc≳g/Hmc\widetilde\Omega_{mc}\gtrsim\sqrt{g/H_{mc}}), the modest and non-decisive vertical temperature difference required, and the height-invariant centrifugal-buoyancy formation time scale of order one minute — were obtained from dry, incompressible Boussinesq direct numerical simulations at Rayleigh numbers roughly 13–15 orders of magnitude below atmospheric values, omitting compressibility, moisture and phase changes, hydrometeor loading, surface roughness, and translatory storm motion. The open problem is to determine the extent to which these three predictions remain valid, and how they are quantitatively modified, when such realistic processes are included — that is, to test the tornadic QC regime in settings closer to a realistic atmosphere and to refine the predictions by incorporating additional mesocyclone processes. No test of these predictions in a setting closer to a realistic atmosphere has been reported; the question remains open.

Background

Most tornadoes form within supercell thunderstorms — long-lived storms dominated by a single rotating updraft — beneath the mesocyclone, a cyclonically rotating column several kilometres wide and roughly 10 km deep. Tornadogenesis, the process by which the near-ground vortex forms and intensifies, remains a central open problem of mesoscale meteorology: classical laboratory and numerical 'tornado simulators' generate tornado-like vortices (TLVs) only by imposing mechanical forcing — fans, prescribed suction, or prescribed buoyancy — that has no counterpart in nature. Horn & Aurnou (2018, 2019) proposed a self-consistent alternative: Coriolis-centrifugal convection (C³), direct numerical simulation (DNS) of convection in a rotating cylinder heated from below and cooled from above, where the cylinder represents the mesocyclone and the imposed rotation rate is the mesocyclone's own angular velocity rather than Earth's. Within the Oberbeck–Boussinesq approximation (density variations retained only in the buoyancy terms), the radial momentum equation then contains a centrifugal buoyancy term: the centrifugal force acting on thermally perturbed density drives lighter fluid inward near the hot bottom and outward near the cold top. The key control parameters are the Rayleigh number RaRa (buoyant driving versus diffusion), the Prandtl number PrPr (momentum versus thermal diffusion), the gravitational Rossby number Ro∥=τΩ/τffRo_\parallel=\tau_\Omega/\tau_{\mathrm{ff}} (Coriolis versus free-fall buoyant acceleration, with τΩ=1/(2Ω)\tau_\Omega=1/(2\Omega) the Coriolis time and τff\tau_{\mathrm{ff}} the free-fall time), the Froude number Fr=Ω2R/gFr=\Omega^2R/g (centrifugal acceleration versus gravity), and the radius-to-height aspect ratio γ=R/H\gamma=R/H. Time-scale arguments identify four dynamical regimes with boundaries Ro∥≃5.5 Pr−1/2Ra−1/6Ro_\parallel\simeq5.5\,Pr^{-1/2}Ra^{-1/6}, Ro⊥≃5.5 Pr−1/2Ra−1/6Ro_\perp\simeq5.5\,Pr^{-1/2}Ra^{-1/6} (Ro⊥Ro_\perp the centrifugal Rossby number), and Fr≃γFr\simeq\gamma; the ratio χ=Fr/γ\chi=Fr/\gamma, called the superfroudeality, measures centrifugal against gravitational buoyancy, and χ≳1\chi\gtrsim1 marks centrifugally dominated flow. The regimes are: three-dimensional (3D, rotation dynamically unimportant), quasi-geostrophic (QG, Coriolis–pressure balance), Coriolis-centrifugal (CC, a gradient-wind-type three-term balance), and quasi-cyclostrophic (QC), where the pressure gradient is balanced mainly by centrifugal buoyancy with Coriolis forces secondary but non-negligible. Horn & Aurnou (2021) showed by DNS (Ra=107Ra=10^7–10910^9) that TLVs form self-consistently — with intensification of the central vortex by more than an order of magnitude, an eye-like central pressure drop, and realistic morphologies including multiple vortices — only within the QC regime and its immediate border regions. Translating the boundaries to a natural mesocyclone of height Hmc≈12H_{mc}\approx12 km yields three predictions: (i) tornado-bearing flow requires Fr≳γFr\gtrsim\gamma, equivalently a critical mesocyclone angular rotation rate Ω~mc≳g/Hmc≈3×10−2 s−1\widetilde\Omega_{mc}\gtrsim\sqrt{g/H_{mc}}\approx3\times10^{-2}\,\mathrm{s^{-1}}, a much more restrictive condition than the corresponding temperature-difference threshold; (ii) the required vertical (potential) temperature difference Δmc\Delta_{mc} is modest and not the decisive factor; and (iii) TLV formation occurs almost simultaneously at all heights on the radius-independent centrifugal-buoyancy time scale τcb=1/(αΔmcΩmc2)\tau_{cb}=\sqrt{1/(\alpha\Delta_{mc}\Omega_{mc}^2)} (α\alpha the thermal expansivity), giving a height-invariant formation time of order one minute (≈65 s for representative estimates), consistent with observational estimates of tornado formation times. These predictions rest, however, on idealized dry, incompressible DNS: the atmospheric Rayleigh number is estimated as Ramc∼6×1021Ra_{mc}\sim6\times10^{21} versus Ra≤109Ra\le10^9 reached in the DNS (a gap of roughly 13–15 orders of magnitude, so a higher level of turbulence is expected but unverified), the control parameters are held fixed whereas they evolve in time in nature, and several physical processes are absent: compressibility, condensation and evaporation and other phase changes, hydrometeors (liquid and ice water loading), dust, surface roughness, vibration-induced boundary-layer destabilization, and translatory storm motion. The paper closes by stating the authors' intent to test the validity of the tornadic QC regime in settings closer to a realistic atmosphere and to refine the predictions by including additional mesocyclone processes — the question posed here.

Problem Statement

Determine the extent to which the quasi-cyclostrophic (QC) regime predictions for tornado-like-vortex (TLV) formation — the TLV-existence regime boundary Fr≳γFr\gtrsim\gamma (the Froude number Fr=Ω2R/gFr=\Omega^2R/g, the ratio of centrifugal to gravitational acceleration, exceeding the radius-to-height aspect ratio γ=R/H\gamma=R/H; equivalently superfroudeality χ=Fr/γ≃1\chi=Fr/\gamma\simeq1, and equivalently the critical mesocyclone angular rotation rate Ω~mc≳g/Hmc≈3×10−2 s−1\widetilde\Omega_{mc}\gtrsim\sqrt{g/H_{mc}}\approx3\times10^{-2}\,\mathrm{s^{-1}} for a 12 km deep mesocyclone, together with the associated gravitational and centrifugal Rossby-number requirements), the claim that the required vertical temperature difference Δmc\Delta_{mc} is modest and not the decisive factor, and the height-invariant formation time scale τcb=1/(αΔmcΩmc2)\tau_{cb}=\sqrt{1/(\alpha\Delta_{mc}\Omega_{mc}^2)} of order one minute (α\alpha the thermal expansion coefficient, Δmc\Delta_{mc} the vertical temperature difference across the mesocyclone, Ωmc\Omega_{mc} its angular rotation rate) — remain valid, and how they are quantitatively modified, when the physical processes omitted in the idealized Coriolis-centrifugal convection (C³) simulations are included: compressibility, moisture with condensation/evaporation and phase changes, hydrometeor loading, surface roughness, and translatory storm motion. In the source's own words, this is the task of testing the tornadic QC regime in settings closer to a realistic atmosphere and refining the predictions by incorporating additional mesocyclone processes, thereby establishing whether centrifugal buoyancy and the quasi-cyclostrophic balance genuinely control whether a mesocyclone becomes tornadic or remains non-tornadic. These three predictions are independently refutable, and the omitted processes can be examined individually; assessing a strict subset of the predictions or of the processes yields a partial answer to the open problem, whereas a complete resolution assesses all three predictions under the listed realistic processes.

References

  1. Susanne Horn, Jonathan M. Aurnou, 'Tornado-like vortices in the quasi-cyclostrophic regime of Coriolis-centrifugal convection', Journal of Turbulence 22, 297–324 (2021). DOI: 10.1080/14685248.2021.1898624; arXiv:2103.01167. https://arxiv.org/abs/2103.01167
  2. Susanne Horn, Jonathan M. Aurnou, 'Regimes of Coriolis-Centrifugal Convection', Physical Review Letters 120, 204502 (2018). DOI: 10.1103/PhysRevLett.120.204502. https://doi.org/10.1103/PhysRevLett.120.204502
  3. Susanne Horn, Jonathan M. Aurnou, 'Rotating convection with centrifugal buoyancy: Numerical predictions for laboratory experiments', Physical Review Fluids 4, 073501 (2019). DOI: 10.1103/PhysRevFluids.4.073501. https://doi.org/10.1103/PhysRevFluids.4.073501
  4. M. C. Navarro, D. Castaño, H. Herrero, 'Determining the morphology of tornado-like vortices depending on thermal gradients: A numerical study', Physics of Fluids 35, 063605 (2023). DOI: 10.1063/5.0145706. https://doi.org/10.1063/5.0145706
  5. Yun-Bing Hu, Lin Sun, Ke-Qing Xia, 'Effects of weak centrifugal force in turbulent rotating thermal convection', Journal of Fluid Mechanics 1030, A26 (2026). DOI: 10.1017/jfm.2026.11234. https://doi.org/10.1017/jfm.2026.11234
  6. Brett Roberts, Ming Xue, Daniel T. Dawson, 'The Effect of Surface Drag Strength on Mesocyclone Intensification and Tornadogenesis in Idealized Supercell Simulations', Journal of the Atmospheric Sciences 77, 1699–1721 (2020). DOI: 10.1175/jas-d-19-0109.1. https://doi.org/10.1175/jas-d-19-0109.1
  7. Wei Huang, Ming Xue, 'What Forces the Rapid Vertical Acceleration and Vorticity Intensification near Ground in Tornadoes? Diagnostic Analysis Based on a Numerically Simulated Real Tornado', Journal of the Atmospheric Sciences 82, 2541–2568 (2025). DOI: 10.1175/jas-d-25-0033.1. https://doi.org/10.1175/jas-d-25-0033.1