Linear and nonlinear Alfvén wave propagation in compressible MHD plasmas

2020 ◽  
Vol 34 (25) ◽  
pp. 2050272
Author(s):  
Zhong-Zheng Li ◽  
Juan-Fang Han ◽  
Fang-Ping Wang ◽  
Zheng-Wu Chen ◽  
Li-Qiang Xie ◽  
...  
Keyword(s):  
Solitary Wave ◽  
Fluid Model ◽  
Wave Train ◽  
Low Frequency ◽  
Wave Theory ◽  
Finite Amplitude ◽  
Alfven Wave ◽  
Linear Wave ◽  
Linear Wave Theory ◽  
Frequency Harmonic

Evolution of both low-frequency harmonic Alfvén wave train and Alfvén solitary wave is studied by using the compressible MHD fluid model. A critical point is found at which linear wave theory should be replaced by a nonlinear one. A small, but finite amplitude Alfvén solitary wave is numerically found. The head-on collision between an Alfvén wave train and an Alfvén solitary wave is also numerically investigated. An interesting result is that there is no phase shift for both colliding waves which is different from that between two KdV solitary waves.

A Phase-Amplitude Iteration Scheme for the Optimization of Deterministic Wave Sequences

2009 ◽  
Author(s):  
Christian Schmittner ◽  
Sascha Kosleck ◽  
Janou Hennig
Keyword(s):  
Target Location ◽  
Wave Train ◽  
Target Position ◽  
Wave Theory ◽  
Iteration Scheme ◽  
Linear Wave ◽  
Linear Wave Theory ◽  
Wave Basin ◽  
Wave Maker ◽  
Phase Amplitude

For the deterministic investigation of extreme events like capsizing, broaching or wave impacts, methods for the generation of deterministic wave sequences are required. These wave sequences can be derived from full scale measurements, numerical simulations or other sources. Most methods for the generation of deterministic wave sequences rely as a backbone on linear wave theory for the backwards transformation of the wave train from the target position in the wave basin to the position of the wave maker. This implies that nonlinear wave effects are not covered to full extend or they are completely neglected. This paper presents a method to improve the quality of the generated wave train via an experimental optimization. Based on a first wave sequence generated with linear wave theory and measured in the wave basin, the phases and amplitudes of the wave maker control signal are modified in frequency domain. The iteration scheme corrects both, shifts in time and in location, resulting in an improved deterministic wave train at the target location. The paper includes results of this method from three different basins with different types of wave generators, water depth and model scales. In addition, this method is applied to a numerical wave tank where the waves can be optimized before the actual basin testing.

Optimization of Short-Crested Deterministic Wave Sequences via a Phase-Amplitude Iteration Scheme

2012 ◽  
Author(s):  
Christian Schmittner ◽  
Janou Hennig
Keyword(s):  
Target Location ◽  
Wave Train ◽  
Target Position ◽  
Wave Theory ◽  
Iteration Scheme ◽  
Linear Wave ◽  
Linear Wave Theory ◽  
Wave Basin ◽  
Wave Maker ◽  
Phase Amplitude

For the deterministic investigation of rare phenomena like capsizing, broaching or wave impacts, methods for the generation of deterministic wave sequences are required. These wave sequences can be derived from full scale measurements, numerical simulations or other sources. Most methods for the generation of deterministic wave sequences rely as a backbone on linear wave theory for the upstream transformation of the wave train from the target position in the wave basin to the position of the wave maker. This implies that nonlinear wave effects are not covered to a full extend or completely neglected. This paper presents the extension of a method for the generation of deterministic waves presented during OMAE 2009. The method improves the quality of the generated wave train via an experimental optimization. Based on a first wave sequence generated with linear wave theory and measured in the wave basin, the phases and amplitudes of the wave maker control signal are modified in frequency domain. The iteration scheme corrects for both shifts in time and in location resulting in an improved deterministic wave train at the target location. The method is extended to short-crested seas. The paper includes results of this method applied to a 3D wave basin.

Nonlinear Waves in Strings: The Barrage Balloon Problem

1998 ◽  
Vol 65 (1) ◽  
pp. 141-149
Author(s):  
J. F. Hall
Keyword(s):  
World War Ii ◽  
Nonlinear Waves ◽  
Wave Reflection ◽  
Wave Theory ◽  
P Wave ◽  
Linear Wave ◽  
Geometrically Nonlinear ◽  
World War ◽  
Linear Wave Theory ◽  
Important Solution

This paper develops a theory for geometrically nonlinear waves in strings and presents analytical solutions for a traveling kink, generation of a geometric wave with its accompanying P wave, reflection of a kink at a fixed support and at a smooth sliding support, and interaction of a P wave and a kink. Conditions that must be satisfied for linear wave theory to hold are derived. The nonlinear theory is demonstrated by extending an historically important solution of the barrage balloon problem that was obtained during World War II.

scholarly journals Reduced models accounting for parallel magnetic perturbations: gyrofluid and finite Larmor radius–Landau fluid approaches

2016 ◽  
Vol 82 (6) ◽  
Author(s):  
E. Tassi ◽  
P. L. Sulem ◽  
T. Passot
Keyword(s):  
Fluid Model ◽  
Collisionless Plasma ◽  
Low Frequency ◽  
Wave Model ◽  
Plasma Phys ◽  
Alfven Wave ◽  
Larmor Radius ◽  
Closure Relation ◽  
Reduced Models ◽  
Finite Larmor Radius

Reduced models are derived for a strongly magnetized collisionless plasma at scales which are large relative to the electron thermal gyroradius and in two asymptotic regimes. One corresponds to cold ions and the other to far sub-ion scales. By including the electron pressure dynamics, these models improve the Hall reduced magnetohydrodynamics (MHD) and the kinetic Alfvén wave model of Boldyrev et al. (2013 Astrophys. J., vol. 777, 2013, p. 41), respectively. We show that the two models can be obtained either within the gyrofluid formalism of Brizard (Phys. Fluids, vol. 4, 1992, pp. 1213–1228) or as suitable weakly nonlinear limits of the finite Larmor radius (FLR)–Landau fluid model of Sulem and Passot (J. Plasma Phys., vol 81, 2015, 325810103) which extends anisotropic Hall MHD by retaining low-frequency kinetic effects. It is noticeable that, at the far sub-ion scales, the simplifications originating from the gyroaveraging operators in the gyrofluid formalism and leading to subdominant ion velocity and temperature fluctuations, correspond, at the level of the FLR–Landau fluid, to cancellation between hydrodynamic contributions and ion finite Larmor radius corrections. Energy conservation properties of the models are discussed and an explicit example of a closure relation leading to a model with a Hamiltonian structure is provided.

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