Generation Model of a Spatially Limited Vortex
in a Stratified Unstable Atmosphere

O. G. Onishchenko; Онищенко О. Г.; S. N. Artekha; Артеха С. Н.; F. Z. Feygin; Фейгин Ф. З.; N. M. Astafieva; Астафьева Н. М.

doi:10.31857/S0016794023600047

Generation Model of a Spatially Limited Vortex in a Stratified Unstable Atmosphere

Authors: Onishchenko O.G.¹, Artekha S.N.², Feygin F.Z.¹, Astafieva N.M.²
Affiliations:
1. Schmidt Institute of Physics of the Earth, Russian Academy of Sciences
2. Space Research Institute, Russian Academy of Sciences
Issue: Vol 63, No 4 (2023)
Pages: 511-519
Section: Articles
URL: https://ogarev-online.ru/0016-7940/article/view/134742
DOI: https://doi.org/10.31857/S0016794023600047
EDN: https://elibrary.ru/OUEAFP
ID: 134742

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Abstract
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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.

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