Nonlinear vortex solution for the inner region of a galaxy

Vukcevic, Miroslava

doi:10.1093/mnras/stz245

Cited by 4 publications

(12 citation statements)

References 14 publications

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“…Here, we underline difference between the Rossby waves derived using so-called geostrophic approximation for number of fluids, planetary atmospheres or plasma drift waves (Sommeria et al, 1988;Marcus, 1989;Hasegawa et al, 1979), and nonlinear soliton wave solution discussed by Petviashvili (1983) and Vukcevic (2019). The first reason for different structure comes from different dispersion relations derived in linearized problem.…”

Section: Drift Approximationmentioning

confidence: 91%

“…Assumption of the stratified stable ionospheric layer involves the Brunt-Väisälä frequency which is fast comparing to large-scale horizontal motion that will be considered here using drift approximation. We will show that the general scalar gravitational potential is equivalent to the effective height of shallow water theory within approximation of Poisson's equation as it was proposed by Vukcevic (2019). Within that approximation, scalar potential is evaluated as two-dimensional denoted by φ, while volume density is evaluated by surface density σ and pressure as two-dimensional pressure denoted by p. Details of Poisson's equation approximation are given in Appendix A.…”

Section: Basic Equationsmentioning

confidence: 94%

“…As far as the gravitational force is concerned, the ionosphere is influenced by the Earth's gravitation in vertical direction but, for the first time here, we add the Poisson's equation for gravitational potential of the neutral gas, relevant for this geometry, on contrary to usual approach based on assumption of shallow water theory (Kaladze et al, 2004), or using stream function description for incompressible fluid (Kaladze, 1998). We use finite thickness approximation in order to estimate gravity influence on the ionospheric gas dynamics, not only in vertical direction, but mainly in horizontal plain, relevant for vortex soliton formation (Vukcevic, 2019). Assumption of shallow water theory is just a consequence of general Poisson's equation, approximated in horizontal plain, and it will be shown in this work.…”

Section: Basic Equationsmentioning

confidence: 99%

“…(7). Three-dimensional Poisson's equation is evaluated in two-dimensional plane geometry, in the neighborhood of z = z 0 as proposed by Vukcevic (2019), involving thickness of the plain via functions A and B.…”

Section: Drift Approximationmentioning

confidence: 99%

“…The conventional Lin-Shu approximation for infinitely thin disk corresponds to the limit of B = 0 which is obtained for g(z) = δ(z). All details about the normalization of the variables and separation of ambient and fluctuation parts are given in the Vukcevic (2019). In order to obtain Eq.…”

Section: (A2)mentioning

confidence: 99%

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Nonlinear vortex solution for perturbations in the Earth’s Ionosphere

Vukcevic¹

2019

Preprint

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Abstract. There are many observational evidences of different fine structures in the ionosphere and magnetosphere of the Earth. Such structures are created and evolve as a perturbation of the ionosphere’s parameters. Instead of dealing with number of linear waves, we propose to investigate and follow up the perturbations in the ionosphere by dynamics of soliton structure. Apart of the fact that it is more accurate solution, the advantage of soliton solution is its localization in space and time as consequence of balance between nonlinearity and dispersion. The existence of such structure is driven by the properties of the medium. We derive necessary condition for having nonlinear soliton wave, taking the vortex shape, as description of ionosphere parameters perturbation. We employ magnetohydrodynamical description for the ionosphere in plane geometry, including rotational effects, magnetic field effects via ponderomotive force, pressure and gravitational potential effects, treating the problem self-consistently and nonlinearly. In addition, we consider compressible perturbation. As a result, we have obtained that Coriolis force and magnetic force at one side, and pressure and gravity on the other side, determine dispersive properties. Dispersion at higher latitudes is mainly driven by rotation, while near the equator, within the E and F-layer of ionosphere, magnetic field modifies the soliton solution. Also, very general description of the ionosphere results in the conclusion that the unperturbed thickness of the ionosphere layer cannot be taken as ad hoc assumption, it is rather consequence of equilibrium property, which is shown in this calculation.

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Section: Drift Approximationmentioning

confidence: 91%

Section: Basic Equationsmentioning

confidence: 94%

Section: Basic Equationsmentioning

confidence: 99%

Section: Drift Approximationmentioning

confidence: 99%

Section: (A2)mentioning

confidence: 99%

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Nonlinear vortex solution for perturbations in the Earth’s Ionosphere

Vukcevic¹

2019

Preprint

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The Spiral Galaxies Flat Rotational Velocity Curve Explained by the Constant Group Velocity of a Nonlinear Density Wave

Vukcevic

2021

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The rotation velocity curves of stars in galaxies, the motions of pairs of galaxies, and the behavior of galaxies in clusters and super-clusters all indicate that there is a lack of mass on different scales in the universe. In this paper, we derive the expression for rotational velocity using the nonlinear density wave theory considering only stellar components and we show that such theory can support the observed flat rotational velocity curve due to the main property of the soliton wave, which is a constant group velocity of the wave. The surface mass density (SMD) function, used to derive gravitational potential gradient and rotational velocity, is not assumed but rather derived as a solution of the nonlinear Srödinger equation, on the contrary to the widely used, in the literature, exponential disk approximation. Three parameters relevant to the curve shape are the intensities of equilibrium SMD, the amplitude of the wave, and total angular velocity or differential rotation, equivalently. Since the shape of the rotational velocity is highly sensitive to the mentioned parameters, this theory eventually provides a method for a very accurate estimation of galaxy mass and angular velocity as well.

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Nonlinear Density Wave Theory in a Gaseous Disk

Vukcevic

2023

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A nonlinear solution for the gaseous component of a galactic disk has been derived self-consistently using fluid description and reductive perturbation theory. We show that gas follows a spiral pattern, similarly to the stellar component; but the spirals are slightly separated due to different relevant parameters, as observations suggest. This analytical solution provides an additional contribution to a better understanding of rotation velocity curves of spiral galaxies. Since the proposed approach, and consequently solution, can be used in various astrophysical dynamical systems, we keep as general as possible a form of the calculus. We underline differences between the stellar and gaseous cases, and we apply this solution roughly on the gaseous disk component dynamics pointing out the importance of the nonlinear approach.

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Nonlinear vortex solution for the inner region of a galaxy

Cited by 4 publications

References 14 publications

Nonlinear vortex solution for perturbations in the Earth’s Ionosphere

Nonlinear vortex solution for perturbations in the Earth’s Ionosphere

The Spiral Galaxies Flat Rotational Velocity Curve Explained by the Constant Group Velocity of a Nonlinear Density Wave

Nonlinear Density Wave Theory in a Gaseous Disk

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