Abstract
This paper presents a new model for the generation of axisymmetric concentrated vortices. The solution of a nonlinear equation for internal gravity waves in an unstable stratified atmosphere is obtained and analyzed within the framework of ideal hydrodynamics. The corresponding expressions describing the dependences on the radius for the radial and vertical velocity components in the inner and outer regions of the vortex include combinations of Bessel functions and modified Bessel functions. The proposed new nonlinear analytical model makes it possible to study the structure and nonlinear dynamics of vortices in the radial and vertical regions. The vortex is limited in height. The maximum vertical velocity component is reached at a certain height. Below this height, radial flows converge towards the axis, and above it, an outflow occurs. The resulting instability in the stratified atmosphere leads to an increase in the radial and vertical velocity components according to the hyperbolic sine law, which turns into exponential growth. The characteristic growth time is determined by the inverse growth rate of the instability. The formation of vortices with finite velocity components, which increase with time, is analyzed. The radial structure of the azimuthal velocity is determined by the structure of the initial perturbation and can change with height. The maximum rotation is reached at a certain height. The growth of the azimuth velocity occurs according to a super-exponential law.
Similar content being viewed by others
REFERENCES
Balme, M. and Greeley, R., Dust devils on Earth and Mars, Rev. Geophys., 2006, p. RG3003.
Battaglia, F., Rehm, R.G., and Baum, H.R., The fluid mechanics of fire whirls: An inviscid model, Phys. Fluids, 2000, vol. 12, pp. 2859–2867.
Church, C.R., Snow, J.T., Baker, G.L., and Agee, E.M., Characteristics of tornado-like vortices as a function of swirl ratio: A laboratory investigation, J. Atmos. Sci., 1979, vol. 36, pp. 1755–1776.
Horton, W., Miura, H., Onishchenko, O., Couedel, L., Arnas, C., Escarguel, A., Benkadda, S., and Fedun, V., Dust devil dynamics, J. Geophys. Res.: Atmos., 2016, vol. 121, pp. 7197–7214.
Ives, R.L., Behavior of dust devils, Bull. Am. Meteorol. Soc., 1947, vol. 28, pp. 168–174.
Justice, A.A., Seeing the inside of a tornado, Mon. Weather Rev., 1930, vol. 58, no. 5, pp. 205–206.
Larichev, V.D. and Reznik, G.M., On two-dimensional solitary Rossby waves, Dokl. Akad. Nauk SSSR, 1976, vol. 231, pp. 1077–1079.
Nalivkin, D.V., Hurricanes, storms, and tornadoes, in Geographic Characteristics and Geological Activity, Rotterdam: A.A. Balkema, 1983.
Onishchenko, O.G., Horton, W., Pokhotelov, O.A., and Stenflo, L., Dust devil generation, Phys. Scr., 2014, vol. 89, p. 075606.
Onishchenko, O., Pokhotelov, O., Horton, W., and Fedun, V., Dust devil vortex generation from convective cells, Ann. Geophys., 2015, vol. 33, pp. 1343–1347.
Onishchenko, O.G., Horton, W., Pokhotelov, O.A., and Fedun, V., Explosively growing vortices of unstably stratified atmosphere, J. Geophys. Res.:: Atmos., 2016, vol. 121, pp. 11–264.
Onishchenko, O.G., Pokhotelov, O.A., Astaf’eva, N.M., Horton, W., and Fedun, V.N., Structure and dynamics of concentrated mesoscale vortices in planetary atmospheres, Phys.-Usp., 2020, vol. 63, pp. 683–697.
Raasch, S. and Franke, T., Structure and formation of dust devil-like vortices in the atmospheric boundary layer: A high-resolution numerical study, J. Geophys. Res.: Atmos., 2011, vol. 116, p. D16120.
Rafkin, S., Jemmett-Smith, B., Fenton, L., Lorenz, R., Takemi, T., Ito, J., and Tyler, D., Dust devil formation, Space Sci. Rev., 2016, vol. 203, pp. 183–207.
Rennó, N.O., Burkett, M.L., and Larkin, M.P., A simple thermodynamical theory for dust devils, J. Atmos. Sci., 1998, vol. 55, pp. 3244–3252.
Rennó, N.O., Abreu, V.J., Koch, J., Smith, P.H., Hartogensis, O.K., De Bruin, H.A.R., Burose, D., Delory, G.T., Farrell, W.M., and Watts, C.J., MATADOR 2002: A pilot field experiment on convective plumes and dust devils, J. Geophys. Res.: Planets, 2004, vol. 109, p. E07001.
Sinclair, P.C., General characteristics of dust devils, J. Appl. Meteorol., 1969, vol. 8, pp. 32–45.
Sinclair, P.C., The lower structure of dust devils, J. Atmos. Sci., 1973, vol. 30, pp. 1599–1619.
Stenflo, L., Acoustic solitary vortices, Phys. Fluids, 1987, vol. 30, pp. 3297–3299.
Stenflo, L., Acoustic gravity vortices, Phys. Scr., 1990, vol. 41, p. 641.
Thorarinsson, S. and Vonnegut, B., Whirlwinds produced by the eruption of Surtsey Volcano, Bull. Am. Meteorol. Soc., 1964, vol. 45, no. 8, pp. 440–444.
Tohidi, A., Gollner, M.J., and Xiao, H., Fire whirls, Annu. Rev. Fluid Mech., 2018, vol. 50, pp. 187–213.
Funding
The work was supported by the State task of the Institute of Physics of the Earth Russian Academy of Sciences and the state task on the “Monitoring” subject of fundamental scientific research of IKI RAS (122042500031-8).
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
The authors declare that they have no conflicts of interest.
Rights and permissions
About this article
Cite this article
Onishchenko, O.G., Artekha, S.N., Feygin, F.Z. et al. Generation Model of a Spatially Limited Vortex in a Stratified Unstable Atmosphere. Geomagn. Aeron. 63, 464–472 (2023). https://doi.org/10.1134/S0016793223600340
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0016793223600340