Vortices evolution in ideal (M)HD

2021 ◽  
Author(s):  
José Roberto Canivete Cuissa ◽  
Oskar Steiner
Keyword(s):  
Evolution Equation ◽  
Solar Atmosphere ◽  
Vortex Dynamics ◽  
Shear Flows ◽  
Dynamical Equation ◽  
Space Plasma ◽  
Optimal Criterion ◽  
Swirling Strength ◽  
Vortex Tubes

<p>Vortices and vortex tubes are ubiquitous in the solar atmosphere and space plasma. In order to identify vortices and to study their evolution, we seek a suitable mathematical criterium for which a dynamical equation exists. So far, the only option available is given by the vorticity, which however is not the optimal criterion since it can be biased by shear flows. Therefore, we look at another criterion, the swirling strength, for which we found an evolution equation, which we suggest as a novel tool for the analysis of vortex dynamics in (magneto-)hydrodynamics. We highlight a few results obtained by applying the swirling strength and its dynamical equation to simulations of the solar atmosphere.</p>

scholarly journals Vortices evolution in the solar atmosphere

2020 ◽  
Vol 639 ◽  
pp. A118
Author(s):  
José R. Canivete Cuissa ◽  
Oskar Steiner
Keyword(s):  
Evolution Equation ◽  
Turbulent Flows ◽  
Solar Atmosphere ◽  
Evolution Equations ◽  
Dynamical Equation ◽  
Numerical Models ◽  
Vortex Identification ◽  
Wide Range ◽  
Swirling Strength ◽  
Hydrodynamical Simulations

Aims. We study vortex dynamics in the solar atmosphere by employing and deriving the analytical evolution equations of two vortex identification criteria. Methods. The two criteria used are vorticity and the swirling strength. Vorticity can be biased in the presence of shear flows, but its dynamical equation is well known; the swirling strength is a more precise criterion for the identification of vortical flows, but its evolution equation is not known yet. Therefore, we explore the possibility of deriving a dynamical equation for the swirling strength. We then apply the two equations to analyze radiative magneto-hydrodynamical simulations of the solar atmosphere produced with the CO5BOLD code. Results. We present a detailed review of the swirling strength criterion and the mathematical derivation of its evolution equation. This equation did not exist in the literature before and it constitutes a novel tool that is suitable for the analysis of a wide range of problems in (magneto-)hydrodynamics. By applying this equation to numerical models, we find that hydrodynamical and magnetic baroclinicities are the driving physical processes responsible for vortex generation in the convection zone and the photosphere. Higher up in the chromosphere, the magnetic terms alone dominate. Moreover, we find that the swirling strength is produced at small scales in a chaotic fashion, especially inside magnetic flux concentrations. Conclusions. The swirling strength represents an appropriate criterion for the identification of vortices in turbulent flows, such as those in the solar atmosphere. Moreover, its evolution equation, which is derived in this paper, is pivotal for obtaining precise information about the dynamics of these vortices and the physical mechanisms responsible for their production and evolution. Since this equation is available, the swirling strength is now the ideal quantity to study the dynamics of vortices in (magneto-)hydrodynamics.

scholarly journals Solar Vortex Tubes: Vortex Dynamics in the Solar Atmosphere

2020 ◽  
Vol 898 (2) ◽  
pp. 137 ◽  
Author(s):  
Suzana S. A. Silva ◽  
Viktor Fedun ◽  
Gary Verth ◽  
Erico L. Rempel ◽  
Sergiy Shelyag
Keyword(s):  
Solar Atmosphere ◽  
Vortex Dynamics ◽  
Vortex Tubes

scholarly journals Self-consistent stationary MHD shear flows in the solar atmosphere as electric field generators

2014 ◽  
Vol 569 ◽  
pp. A44 ◽  
Author(s):  
D. H. Nickeler ◽  
M. Karlický ◽  
T. Wiegelmann ◽  
M. Kraus
Keyword(s):  
Electric Field ◽  
Solar Atmosphere ◽  
Shear Flows ◽  
Self Consistent

Vortex dynamics of fiber-laden free shear flows

2005 ◽  
Vol 127 (2-3) ◽  
pp. 73-87 ◽  
Author(s):  
F. Sharifi ◽  
J. Azaiez
Keyword(s):  
Vortex Dynamics ◽  
Shear Flows

scholarly journals The fascinating world of the Landau–Lifshitz–Gilbert equation: an overview

2011 ◽  
Vol 369 (1939) ◽  
pp. 1280-1300 ◽  
Author(s):  
M. Lakshmanan
Keyword(s):  
Evolution Equation ◽  
Elliptic Function ◽  
Nonlinear Evolution Equation ◽  
Dynamical Equation ◽  
Nonlinear Evolution ◽  
Spin Torque ◽  
Physical Systems ◽  
Space Curves ◽  
Points Of View ◽  
Spatio Temporal

The Landau–Lifshitz–Gilbert (LLG) equation is a fascinating nonlinear evolution equation both from mathematical and physical points of view. It is related to the dynamics of several important physical systems such as ferromagnets, vortex filaments, moving space curves, etc. and has intimate connections with many of the well-known integrable soliton equations, including nonlinear Schrödinger and sine-Gordon equations. It can admit very many dynamical structures including spin waves, elliptic function waves, solitons, dromions, vortices, spatio-temporal patterns, chaos, etc. depending on the physical and spin dimensions and the nature of interactions. An exciting recent development is that the spin torque effect in nanoferromagnets is described by a generalization of the LLG equation that forms a basic dynamical equation in the field of spintronics. This article will briefly review these developments as a tribute to Robin Bullough who was a great admirer of the LLG equation.

An amplitude-evolution equation for linearly unstable modes in stratified shear flows

1982 ◽  
Vol 117 ◽  
pp. 457-471 ◽  
Author(s):  
L. Engevik
Keyword(s):  
Evolution Equation ◽  
Couette Flow ◽  
Shear Flows ◽  
Temporal Evolution ◽  
Amplitude Equation ◽  
Second Order ◽  
Buoyancy Frequency ◽  
Density Profiles ◽  
Long Wave ◽  
Second Order In Time

A nonlinear amplitude equation of second order in time, which governs the temporal evolution of linearly unstable modes in stratified shear flows, is derived. It applies to a class of flows with continuous velocity and density profiles, and two examples of such flows are studied.One of the flows that is studied is the stratified Couette flow with the buoyancy frequency equal to Qy2, where Q is a constant and y the vertical co-ordinate. The nonlinear amplitude equation is studied for various values of Q.For the Garcia flow the nonlinear amplitude equation for the long-wave modes is evaluated, and it is compared with the corresponding equation in the Kelvin–Helmholtz flow, which has been found previously.

Vorticity and Vortex Dynamics in Complex Turbulent Flows

1987 ◽  
Vol 11 (1) ◽  
pp. 21-35 ◽  
Author(s):  
J.C.R. Hunt
Keyword(s):  
Turbulent Flows ◽  
Vortex Dynamics ◽  
Shear Flows ◽  
Two Dimensional ◽  
Basic Principles ◽  
New Ideas ◽  
Simple Class ◽  
Basic Equations ◽  
Mixing Length Theory ◽  
Line Elements

Some of the basic principles of vortex dynamics arc reviewed in this paper and applied to calculating and understanding various kinds of turbulent flows. After setting out the basic equations and boundary conditions, the different principles are illustrated for special eases where different simplifications are justified. The displacement of two-dimensional vorticity is applied to two-dimensional shear flows over slender shapes (such as humps or hills on surfaces where the ‘triple-deck’ method is explained in terms of vorticity). The general changes of vorticity and velocity are related to the movement of fluid-line elements. A new geometrical proof for the changes in velocity is given. These concepts are applied to distorted turbulent flows (isotropic and anisotropic) and shear flows. Recent results on the forces on and motions of finite fluid volumes in rotational, non-uniform flows are reviewed and it is shown that the inertial or added mass effects are generally of greater importance than the distortion of the vorticity field. This gives some new insight into Prandtl’s mixing length theory. A simple class of interaction between vortices is reviewed to illustrate how the interactions differ depending on the relative strengths of the vortices. Finally, some new ideas are reviewed on vorticity shed from surfaces and how this interacts with vorticity advected onto a body from upstream.

Some Problems in Understanding the Solar Corona

1994 ◽  
Vol 144 ◽  
pp. 1-9
Author(s):  
A. H. Gabriel
Keyword(s):  
Solar Corona ◽  
Solar Atmosphere ◽  
Theoretical Modelling ◽  
Total System ◽  
Major Advance ◽  
X Ray ◽  
Proper Perspective ◽  
Space Observations

The development of the physics of the solar atmosphere during the last 50 years has been greatly influenced by the increasing capability of observations made from space. Access to images and spectra of the hotter plasma in the UV, XUV and X-ray regions provided a major advance over the few coronal forbidden lines seen in the visible and enabled the cooler chromospheric and photospheric plasma to be seen in its proper perspective, as part of a total system. In this way space observations have stimulated new and important advances, not only in space but also in ground-based observations and theoretical modelling, so that today we find a well-balanced harmony between the three techniques.

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