Open problems for the Coriolis-based gas dynamics of destructive atmospheric vortices: simulation fidelity, selection of a persistent vortex, planetary-rotation regimes, and energy feasibility of usage and mitigation

Bautin, Krutova and Obukhov (AIP Conf. Proc. 2027, 030018, 2018) summarized a gas-dynamic research program claiming that the azimuthal (swirling) motion of destructive atmospheric vortices — tornadoes, tropical cyclones and fire whirls — is caused by the Earth's rotation, supported by existence-and-uniqueness theorems for initial–boundary-value problems of the compressible Navier–Stokes system, three-dimensional nonstationary calculations, and pipe experiments producing free (unforced-swirl) vortices. The paper itself acknowledges four unresolved issues: (1) three-dimensional nonstationary computations still display unphysical oscillations, and physically justified constant coefficients of viscosity and heat conductivity together with robust smoothing procedures remain an open methodological problem; (2) in temperature-dominated flows a transient coexistence of two counter-rotating whirlwinds with survival of only one is observed, but the selection mechanism is unresolved; (3) the energy inputs required for tornado/cyclone mitigation, the attainable efficiency of the proposed 'vortical energy generator', and the scale-up from metre-scale pipe experiments to atmospheric scales are unquantified; (4) a systematic catalogue of parameter regimes (characteristic speed $U$, length $L$, and thermodynamic parameters) delineating when centrifugal or Coriolis terms may be neglected versus when they dominate is incomplete. These four questions remain unresolved: the independent literatures on tornadogenesis and fire whirls, while following a different (wind-shear/ambient-vorticity) mechanism, have neither resolved nor quantitatively refuted them.

Background

Destructive atmospheric vortices — tornadoes, tropical cyclones and fire whirls (swirling, fire-driven updrafts) — concentrate enormous rotational kinetic energy in near-surface azimuthal (tangential) motion. A first-principles description treats the air as a compressible, viscous, heat-conducting gas governed by the full (unaveraged) Navier–Stokes system, written in a reference frame rotating with the Earth so that gravity and the Coriolis force $-2\Omega\times v$ (with $\Omega$ the planetary angular-velocity vector and $v$ the gas velocity) appear as body forces. The generation of azimuthal velocity — 'rollup', producing the involute (spiral) inflow pattern of such vortices — is the central phenomenon.

A widespread heuristic compares nonlinear advection, of order $U^2/L$, with the Coriolis acceleration, of order $2\Omega U$, for characteristic speed $U$ and length $L$; equivalently, the Rossby number $Ro=U/(2\Omega L)$. When $Ro\gg 1$ — as for a tornado with $U\sim 10^2$ m/s and $L\sim 10^2$ m, giving $Ro\sim 10^4$ — practitioners typically neglect planetary rotation in the vortex dynamics itself.

The Novosibirsk–Ekaterinburg group of Bautin, Krutova and Obukhov disputes this. Between 2008 and 2018 they developed a gas-dynamic program, summarized in the source paper and the monographs it cites, with three pillars. (i) Theorems: for explicitly posed initial–boundary-value regional problems of the compressible gas-dynamic and full Navier–Stokes systems (for example, flow over an impenetrable plane or in contact with a region at rest), local existence and uniqueness of analytic solutions are proved, and in these solutions rollup appears only when the planetary-rotation terms are retained; its sign is fixed by hemisphere and flow type — counterclockwise for ordinary tornadoes and cyclones in the Northern hemisphere, clockwise for 'fiery tornadoes' (announced analytically in Bautin and Krutova 2012; extended to fire vortices in Bautin, Krutova and Obukhov 2015). (ii) Calculations: a sequence from two-dimensional steady flows to three-dimensional nonstationary supercomputer computations of buoyancy-driven air flows over a lower surface locally heated at multiple regions (in the Bautin and Obukhov 2019 companion study, 19 heated zones gradually raised from an initial 288 K toward 300 °C) identifies a regime in which the azimuthal kinetic energy $\frac{1}{2}\rho v_\theta^2$ overtakes the radial one — proposed as a destructiveness criterion — and reproduces observed inflow-region sizes and times to stationarity, but exhibits unphysical oscillations controlled by artificial constant viscosity and heat-conductivity coefficients together with smoothing procedures. (iii) Experiments: vertical pipes with bottom-to-top fan-driven air flow (the two-metre configuration is described in the published report of Bautin and Makarov's group, 2016) produce self-moving, tornado-like 'free' involute upflows without imposed swirl, above a pipe-diameter threshold stated in the group's reports (metre scale), with a claimed measurable Coriolis influence even at $Ro\approx 7\times 10^4$ ($U=0.5$ m/s, $L=0.05$ m). On this basis the paper proposes early detection of tornado origin, elimination of tornadoes and cyclones with 'reasonable power expenses', and a 'vortical energy generator' harvesting the induced swirl (a design described in the source).

The independent adjacent fields hold a different view. In modern research on tornado formation in supercell thunderstorms, storm rotation arises from tilting and stretching of horizontal vorticity generated by vertical wind shear in the storm environment, concentrated within the parent storm's mesocyclone (its rotating updraft), with planetary rotation entering only at the synoptic scale (Davies-Jones 2015). Fire-whirl formation is dominated by wind and geometry — the concentration of ambient vorticity by the fire's own inflow (Tohidi, Gollner and Xiao 2018) — and counter-rotating vortex pairs are an experimentally verified origin of fire whirls (Shinohara and Matsushima 2012). Classical drain-vortex ('bath-tub vortex') experiments (Shapiro 1962; Trefethen et al. 1965) nevertheless showed that Earth's rotation can determine the sense of a small-scale vortex when the initial motion and parasitic torques are small enough — the physical situation closest to the group's free-upflow pipes. Deliberate modification of intense vortices has a negative engineering record: the hurricane-seeding program Project STORMFURY (1962–1983) was abandoned as ineffective (Willoughby et al. 1985).

Problem Statement

The problem is the set of unresolved issues that Bautin, Krutova and Obukhov explicitly acknowledge as following from their 2018 summary of the Coriolis-based gas dynamics of destructive atmospheric vortices. The four unresolved issues share one objective — completing that program's quantitative account of how destructive atmospheric vortices form, are sustained, and could be used or eliminated:

(1) Simulation fidelity. Establish a methodology for the three-dimensional nonstationary computations of the full Navier–Stokes system on which the program rests: physically justified (rather than tuned) constant coefficients of viscosity and heat conductivity, and robust smoothing procedures, such that the computations are free of the unphysical oscillations currently attributable to numerical-method properties.

(2) Vortex selection in temperature-dominated flows. Explain the mechanism by which, in flows where temperature variations dominate — the setting of the group's full Navier–Stokes computations of air over a lower surface locally heated at multiple regions (19 heated zones raised from an initial 288 K toward 300 °C; Bautin and Obukhov 2019) — transiently coexisting counter-rotating whirlwinds are reduced to a single persistent vortex: what selects the surviving vortex and its direction of rotation.

(3) Energy feasibility of usage and mitigation. Quantify the practical feasibility of the proposed applications: the energy input required to eliminate or mitigate a tornado or tropical cyclone under the paper's gas-dynamic theory; the attainable efficiency of the proposed vortical energy generator; and the scale-up from the laboratory pipe experiments, including the pipe-diameter threshold stated in the group's reports, to atmospheric scales.

(4) Regimes of planetary-rotation influence. Replace the Rossby-number heuristic with a systematic catalogue of parameter regimes — precise ranges of the characteristic speed $U$, the length $L$, and the other flow and thermodynamic parameters — delineating when centrifugal acceleration and Coriolis terms may be neglected and when they dominate.

The four sub-questions are independently posed and independently resolvable: each addresses a distinct part of the program's account, and resolving any one of them is a self-contained contribution toward the shared objective while leaving the others open; an answer may therefore take up one strand, several, or all four.

An answer need not adopt the program's premise that planetary rotation is the sole origin of vortex swirl; the questions may be approached within the program's framework or in relation to alternative-mechanism accounts.

References

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