Two-dimensional self-similarity transformation theory and line rogue waves excitation

The Bineau reduction to scalar form of the equation governing ideal zero-frequency linearized displacements from a hydromagnetic equilibrium possessing a continuous symmetry is performed in ‘universal co-ordinates’, applicable to both the toroidal and helical cases. The resulting generalized Newcomb equation (GNE) has in general a more complicated form than the corresponding one-dimensional equation obtained by Newcomb in the case of circular cylindrical symmetry, but in this cylindrical case we show that the equation can be transformed to that of Newcomb. In the two-dimensional case there is a transformation that leaves the form of the GNE invariant and simplifies the Frobenius expansion about a rational surface, especially in the limit of zero pressure gradient. The Frobenius expansion about a mode rational surface is developed and the connection with Hamiltonian transformation theory is shown. The derivations of the ideal interchange and ballooning criteria from the formalism are discussed.

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Arbitrary shaped acoustic omnidirectional absorber based on transformation theory

International Journal of Modern Physics B ◽

10.1142/s0217979220501118 ◽

2020 ◽

Vol 34 (11) ◽

pp. 2050111

Author(s):

Weikai Xu ◽

Yingchun Tang ◽

Meng Zhang ◽

Wuchao Qi ◽

Wei Wang

Keyword(s):

Numerical Simulations ◽

Elastic Waves ◽

Sound Absorption ◽

Acoustic Absorption ◽

Two Dimensional ◽

Acoustic Path ◽

Transformation Theory ◽

Material Parameters ◽

Arbitrary Geometries ◽

Transformation Acoustics

In this study, an arbitrary shaped acoustic omnidirectional absorber (AOA) is achieved for absorbing incoming acoustic/elastic waves in the ambient environment. Using the transformation acoustics theory, we present a theoretical framework for two-dimensional acoustic path guidance around arbitrary shapes for which the material parameters in the transformed space can be obtained analytically. Results indicate that the transformed space is distorted rather than compressed; numerical simulations confirm that these absorbers exhibit a remarkably large absorption and that the proposed method can control acoustic absorption for arbitrary geometries of interest. This method can potentially be applied to sound absorption and noise control.

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CHAOS AND FRACTAL OF THE GENERAL TWO-DIMENSIONAL QUADRATIC MAP

International Journal of Modern Physics B ◽

10.1142/s0217979208039927 ◽

2008 ◽

Vol 22 (20) ◽

pp. 3461-3471

Author(s):

XINGYUAN WANG

Keyword(s):

Fractal Dimension ◽

General Feature ◽

Strange Attractors ◽

Two Dimensional ◽

Control Parameters ◽

Self Similarity ◽

Boundary Equation ◽

Quadratic Map ◽

Fractal Images ◽

Stable Points

The nature of the stable points of the general two-dimensional quadratic map is considered analytically, and the boundary equation of the first bifurcation of the map in the parameter space is given out. The general feature of the nonlinear dynamic activities of the map is analyzed by the method of numerical computation. By utilizing the Lyapunov exponent as a criterion, this paper constructs the strange attractors of the general two-dimensional quadratic map, and calculates the fractal dimension of the strange attractors according to the Lyapunov exponents. At the same time, the researches on the fractal images of the general two-dimensional quadratic map make it clear that when the control parameters are different, the fractal images are different from each other, and these fractal images exhibit the fractal property of self-similarity.

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Inverse cascade of kinetic energy in two-dimensional β-Plane magnetohydrodynamic turbulence

10.5194/egusphere-egu2020-4497 ◽

2020 ◽

Author(s):

Timofey Zinyakov ◽

Arakel Petrosyan

Keyword(s):

Numerical Simulation ◽

Kinetic Energy ◽

Cascade Process ◽

Two Dimensional ◽

Mhd Turbulence ◽

Self Similarity ◽

Magnetohydrodynamic Turbulence ◽

Zonal Flows ◽

Inverse Cascade ◽

Kolmogorov Spectrum

Numerical studies of two-dimensional &#946;-plane homogeneous magnetohydrodynamic turbulence are presented. The study of the fundamental properties of such turbulence allows understanding the evolution of various astrophysical objects from the Sun and stars to planetary systems, galaxies, and galaxy clusters. Energy spectra and cascade process in two-dimensional &#946;-plane MHD are studied.In this work the equations of two-dimensional magnetohydrodynamics with the Coriolis force in the &#946;-plane approximation are used for the qualitative analysis and numerical simulation of processes in plasma astrophysics. The equations are solved on a square box of edge size 2&#960; with periodic boundary conditions applying a the pseudospectral method using the 2/3 rule for dealiasing. The results of numerical simulation of two-dimensional &#946;-plane MHD turbulence with a spatial resolution of 1024 &#215; 1024 and 4096 &#215; 4096 with different Rossby parameters &#946; and different Reynolds numbers are presented.It is found that only unsteady zonal flows with complex temporal dynamics are formed in two-dimensional &#946;-plane magnetohydrodynamic turbulence. It is shown that flow nonstationarity is due to the appearance of isotropic magnetic islands caused by the Lorentz force in the system. The formation of Iroshnikov&#8211;Kraichnan spectrum is shown in the early stages of evolution of two-dimensional &#946;-plane magnetohydrodynamic turbulence. The self-similarity of the decay of Iroshnikov&#8211;Kraichnan spectrum is studied. On long time scale violation of self-similarity of the decay and formation of Kolmogorov spectrum is discovered. The inverse cascade of kinetic energy, which is characteristic of the detected Kolmogorov spectrum, provides the formation of zonal flows.This work was supported by the Russian Foundation for Basic Research (project no. 19-02-00016).

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