On the Geometry, Velocity, and Energy Characteristics of the Bottom Parts of Tornadoes and Tropical Cyclones

About the authors:

Sergei P. Bautin, Dr. Sci. (Phys.-Math), Professor, Department of Higher and Applied Mathematics, Snezhinsk Physical-Technical Institute, National Research Nuclear University MEPhI (Snezhinsk); eLibrary AuthorID, sbautin@usurt.ru

Irina Yu. Krutova, Cand. Sci. (Phys.-Math.), Head of the Department of Higher and Applied Mathematics, Snezhinsk Physic Institute of the National Research Nuclear University MEPhI; iykrutova@mephi.ru

Olga V. Opryshko, Postgraduate Student, Department of Higher and Applied Mathematics, Snezhinsk Physic Institute of the National Research Nuclear University MEPhI; opryshko_olga@mail.ru

Abstract:

This work aims to present detailed analytical and numerical studies of complex air currents in destructive atmospheric vortices. In particular, since the most of the kinetic energy of tornadoes and tropical cyclones is concentrated in their benthic parts, it is in these regions that the geometry, velocity, and energy characteristics of these flows are considered in detail.

As a mathematical model, a system of equations of gas dynamics and a complete system of Navier-Stokes equations are used, taking into account the action of gravity and Coriolis forces. Due to the initial and boundary conditions, the solutions of the system of differential equations of gas dynamics that take into account the effect of the Coriolis force and simulate air currents in the bottom parts of a tornado and a tropical cyclone are constructed numerically and analytically. The solutions constructed are consistent with the data of field observations of these natural air currents.

When analyzing these solutions, it is strictly mathematically established that part of the kinetic energy of the Earth’s rotation passes into the kinetic energy of the rotational motion of these currents, and the rotational motion has no other sources of energy. It is noted that only those tornadoes whose destructive kinetic energy becomes predominant in the kinetic energy of the entire stream are destructive.

Using the results of experimental and theoretical studies, the erroneousness of the proposal has been shown to ignore the rotation of the Earth for those flows for which the Rossby number is much greater than unity.

The paper also presents calculations of three-dimensional nonstationary flows of a compressible viscous heat-conducting gas, which are the corresponding solutions of the complete system of Navier-Stokes equations with allowance for the action of gravity and Coriolis forces. An initial-boundary problem was posed, the solutions of which simulate an experiment with vertical air blowing up the large diameter pipe. Nonstationary calculations of the velocity and energy characteristics were performed for various vertical blowing velocities up to the exit of the emerging swirling air flow to the stationary self-sustaining mode of operation.

References:

1. Abdubakova L. V., Obukhov A.G. 2014. “Chislennyy raschet termodinamicheskikh parametrov zakruchennogo potoka gaza, initsiirovannogo kholodnym vertikal’nym produvom” [Numerical Calculation of the Thermodynamic Parameters of a Swirling Gas Flow Initiated by a Cold Vertical Blowing]. Izvestiya vysshikh uchebnykh zavedeniy. Neft’ i gaz, no 5, pp. 57-62.
2. Bautin S. P., Obukhov A. G. 2012. Matematicheskoe modelirovanie razrushitel’nykh atmosfernykh vikhrey [Mathematical Modeling of Destructive Atmospheric Vortices]. Novosibirsk: Nauka.
3. Bautin S. P., Krutova I. Yu., Obukhov A. G. 2017. “Matematicheskoe obosnovanie vliyaniya vrashcheniya Zemli na tornado i tropicheskie tsiklony” [Mathematical Substantiation of the Influence of the Earth’s Rotation on Tornadoes and Tropical Cyclones]. Vestnik natsional’nogo issledovatel’skogo yadernogo universiteta “MIFI”. Teoreticheskaya i eksperimental’naya fizika, vol. 6, no 2, pp. 101-107.
4. Bautin S. P., Deryabin S. L., Krutova I. Yu., Obukhov A. G. 2017. Razrushitel’nye atmosfernye vikhri i vrashchenie Zemli vokrug svoey osi [Destructive Atmospheric Vortices and Rotation of the Earth around Its Axis]. Yekaterinburg: Izd-vo UrGUPS.
5. Bautin S. P., Krutova I. Yu., Obukhov A. G., Bautin K. V. 2013. Razrushitel’nye atmosfernye vikhri: teoremy, raschety, eksperimenty [Destructive Atmospheric Vortices: Theorems, Calculations, and Experiments]. Novosibirsk: Nauka; Yekaterinburg: Izd-vo UrGUPS.
6. Bautin S. P. 2008. Tornado i sila Koriolisa [Tornado and the Coriolis Force]. Novosibirsk: Nauka.
7. Bautin S. P. 2009. Kharakteristicheskaya zadacha Koshi i ee prilozheniya v gazovoy dinamike [The Cauchy Problem and Its Applications in Gas Dynamics]. Novosibirsk: Nauka.
8. Varaksin A. Yu., Romash M. E., Kopeytsev V. N. 2011. Tornado [Tornadoes]. Moscow: Fizmatlit.
9. Volkov R. E., Obukhov A.G. 2016. “Metod rasparallelivaniya algoritma chislennogo resheniya polnoy sistemy uravneniy Nav’e-Stoksa” [The Method of Parallelizing the Algorithm for the Numerical Solution of the Complete Navier-Stokes Equations System]. Izvestiya vysshikh uchebnykh zavedeniy. Neft’ i gaz, no 2, pp. 92-98.
10. Volkov R. E., Obukhov A. G. 2016. “Parallel’nye vychisleniya v issledovaniyakh zavisimosti gazodinamicheskikh parametrov voskhodyashchego zakruchennogo potoka gaza ot skorosti produva” [Parallel Computations in Studies of the Dependence of the Gasdynamic Parameters of an Ascending Swirling Gas Flow on the Speed of Blowing]. Izvestiya vysshikh uchebnykh zavedeniy. Neft’ i gaz, no 1, pp. 92-97.
11. Nalivkin D. V. 1984. Smerchi [Tornadoes]. Moscow: Nauka.
12. Emanuel K. A. 2000. “A Statistical Analysis of Tropical Cyclone Intensity”. Journal of the Atmospheric Sciences, vol. 128, pp. 1139-1152.
13. Tatom F. B., Witton S. J. 2009. “The Transfer of Energy from Tornado into the Ground”. Seismological Research Letter, vol. 72, no 1, pp. 12-21.
14. Tous M., Romero R. 2013. “Meteorological Environment Associated with Medicane Development”. International Journal of Climatology, vol. 33, pp. 1-14.