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A new analytical model for the generation of axisymmetric tornado-type vortices has been developed. A solution to the nonlinear equation for the stream function in an unstable stratified atmosphere is obtained and analyzed within the framework of ideal hydrodynamics. The solution is sought by smooth connecting continuous solutions for the internal region ("eye"), the central region ("wall" with maximum velocities) and the external region of the tornado. Expressions describing radial dependences for the radial and vertical velocity components include combinations of Bessel functions. The vortex is spatially localized by radius and height. Convective instability of a stratified atmosphere leads to an increase in the radial and vertical components of velocities according to the hyperbolic sine law. A downward flow is observed near the tornado axis. The maximum speed of the upward flow is achieved at a certain radial distance at a certain height. Below this height, radial flows converge towards the central part of the tornado, and above this height there is an outflow from the "wall" to the axis and to the periphery. The radial structure of the azimuthal velocity is determined by the structure of the initial disturbance and can change with height. Maximum rotation is achieved in the tornado "wall" at a certain height. The increase in azimuthal velocity can occur according to a superexponential law. Possible structures of movements, scenarios for the development of a tornado and its dynamics are discussed., Comment: 36 pages, 11 figures

For analytical description of the initial stage of jet generation in nonequilibrium inhomogeneous plasma in the magnetohydrodynamic approximation, possible generalizations of solutions of the nonlinear equation for the stream function are analyzed. The jet generation model is based on the mechanism of convective instability and the frozen-in condition of magnetic field lines and is characterized by a number of free parameters. The equation for the radial part of the stream function is satisfied by first-order Bessel functions. To satisfy all the conditions near the jet axis and on its periphery, the found solutions are smoothly joined at the boundary. The final analytical solution for the velocity field is applicable to arbitrary values of dimensionless coordinates. The poloidal velocity increases approximately exponentially, and the azimuthal velocity - according to a superexponential law. In this paper, the velocity field of the jet, which consists of seven sections, is calculated. The rotation of the jet turns out to be differential, and to obtain a solution in quadratures for the azimuthal velocity, one can use not only linear but also power dependences on the altitude. For the exponent n < 1, a noticeable increase in the azimuthal velocity with radius is observed immediately from the jet axis, and for n > 1, a region of relative calm is observed near the axis. The jet model is generalized to the case of an arbitrary dependence of the Brunt-V\"ais\"al\"a frequency on the altitude. The corresponding solutions are found for the radial and vertical velocity components. For the initial stage of development, the vertical and azimuthal components of the generated magnetic field of the jet were also found in the work., Comment: 12 pages, 5 figures

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., Comment: 17 pages, 4 figures. arXiv admin note: text overlap with arXiv:2408.14210

In the magnetohydrodynamic approximation, system of equations is proposed which analytically describes the initial stage of origination of axially symmetric directed flows in nonequilibrium stratified plasma. The mechanism of generation is based on the Schwarzschild's convective instability and uses the frozen-in flux condition for magnetic field lines. A solution to the nonlinear equation for the stream function is obtained and analyzed, and it is shown that jets with poloidal velocity fields are generated in such a plasma. The corresponding expressions for the R-dependences of the radial and vertical velocity components in the internal and external regions of the jet include Bessel functions and modified Bessel functions. For jets localized in height and radius, the proposed new nonlinear analytical model makes it possible to study their structure and nonlinear dynamics in the radial and vertical directions. The emerging instability in a stratified plasma leads to an increase in the radial and vertical velocities of flows according to the law of the hyperbolic sine. The characteristic growth time depends on the value of the imaginary part of the Brunt-Vyaisyalya frequency. The formation of jets with finite velocity components increasing with time is analyzed. The radial structure of the azimuthal components is determined by the structure of the initial perturbation and can vary with altitude. Along with studying the dynamics of the velocity field, the change in the vertical magnetic field, as well as the dynamics and structure of the emerging toroidal electric current, are investigated., Comment: 30 pages, 5 figures

The problem of the emergence of wave dispersion due to the heterogeneity of a transmission line (TL) is considered. An exactly solvable model helps to better understand the physical process of a signal passing through a non-uniform section of the line and to compare the exact solution and solutions obtained using various approximate methods. Based on the transition to new variables, the developed approach made it possible to construct exact analytical solutions of telegraph equations with a continuous distribution of parameters, which depend on the coordinate. The flexibility of the discussed model is due to the presence of a number of free parameters, including two geometric factors characterizing the lengths of inhomogeneities in values of the inductance L and of the capacitance C. In the new variables, the spatiotemporal structure of the solutions is described using sine waves and elementary functions, and the dispersion is determined by the formulas of the waveguide type. The dispersive waveguide-like structure characterized by refractive index N and cut-off frequency $\Omega$. The exact expressions for the complex reflection and transmission coefficients are derived. These expressions describe phase shifts for reflected and transmitted waves. The following interesting cases are analyzed: the passage of waves without phase change, the reflectionless passage of waves, and the passage of signals through a sequence of non-uniform sections. The developed mathematical formalism can be useful for the analysis of a wider range of problems., Comment: 20 pages, 10 figures

The crucial part of electromagnetic phenomena in many atmospheric processes is verified by systematized data. The multilayered charged system of clouds represents some dynamically equilibrium structure kept by the ionic and polarization forces. The estimates of acting forces are presented and it is demonstrated the necessity to take into account the plasma-like subsystems, effect on some atmospheric phenomena, including the formation and the maintenance of the structure and characteristics of their movement., Comment: 27 pages, 4 figures, 2 tables

The article is devoted to electromagnetic phenomena in the atmosphere. The set of experimental data on the thunderstorm activity is analyzed. It helps to identify a possible physical mechanism of lightning flashes. This mechanism can involve the formation of metallic bonds in thunderclouds. The analysis of the problem is performed at a microphysical level within the framework of quantum mechanics. The mechanism of appearance of metallic conductivity includes the resonant tunneling of electrons along resonance-percolation trajectories. Such bonds allow the charges from the vast cloud charged subsystems concentrate quickly in lightning channel. The formation of metal bonds in the thunderstorm cloudiness is described as the second-order phase transition. A successive mechanism for the process of formation and development of the lightning channel is suggested. This mechanism is associated with the change in the orientation of crystals in growing electric field. Possible consequences of the quantum-mechanical mechanism under discussion are compared with the results of observations., Comment: 28 pages, 5 figures

Numerous sources produce the ionization impact on the planetary atmosphere. The tropospheric cloudiness therewith is originated at such altitudes, which coincide with places of the maximum of the atmospheric ionization that caused by space radiation. Components of cosmic radiation, penetrating down to the stratospheric and tropospheric altitudes, produce in the first place the ionization of aerosols that brings to subsequent amplifying the activity of atmospheric vortices. The ionized aerosol constituent is of primary importance both in the initiation of plasma vortices and in the concentration of energy-mass by air vortices due to the humidity condensation. The ionization process is cascading, that causes the non-linear impact of penetrating rays, which amplifying with growing the air pollution. Various heterogeneities inside plasma subsystems provoke the random intensification of aperiodic electrostatic disturbances, which can exert a significant action on the development of vortices. Sometimes beaded lightning arises during thunderstorm. Using the approach of the Boltzmann kinetic equation, the characteristics of electrostatic oscillations for non-uniform plasma, are analytically derived. The analytical expressions are obtained for non-magnetized plasma. In the limits of the Earth's atmosphere, these solutions are strictly applicable to the origination of electrostatic modulations along the lines of force of the geomagnetic field and approximately applicable in cases, when the impact of the Earth's magnetic field is negligible. The explicit expressions are deduced both in the hot plasma approximation and in the cold plasma approximation. It is demonstrated that the formation of chain elements of discharge in hot inhomogeneous plasma is defined by the nonmonotonic distribution of charges and fields. At such conditions, the irregularities breaks up into a cellular structure., Comment: 18 pages