Abstract
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 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, $Fr \gtrsim \gamma$. We show that the TLVs that develop in our 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.
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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 $Fr \gtrsim \gamma$ 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 $\widetilde{\Omega}_{mc}\gtrsim 3~\times~\SI{10^{-2}}{s^{-1}}$ 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.
This requires the Froude number to be greater than the radius-to-height aspect ratio, $Fr \gtrsim \gamma$. We show that the TLVs that develop in our 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.
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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 $Fr \gtrsim \gamma$ 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 $\widetilde{\Omega}_{mc}\gtrsim 3~\times~\SI{10^{-2}}{s^{-1}}$ 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.
| Original language | English |
|---|---|
| Pages (from-to) | 297-324 |
| Number of pages | 28 |
| Journal | Journal of Turbulence |
| Volume | 22 |
| Issue number | 4-5 |
| Early online date | 15 Mar 2021 |
| DOIs | |
| Publication status | Published - 2021 |
Bibliographical note
This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of Turbulence on 15/03/2021, available online: http://www.tandfonline.com/10.1080/14685248.2021.1898624Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.
Funder
NSF-EAR Geophysics Program supported this work via awards #1547269 and #1853196.Keywords
- Turbulence
- centrifugal buoyancy
- rotating convection
- tornadoes
ASJC Scopus subject areas
- Computational Mechanics
- Condensed Matter Physics
- Mechanics of Materials
- Physics and Astronomy(all)