Alfvén Complexity

Rempel, Erico L.; Chian, Abraham C.‐L.; Koga, D.; Miranda, Rodrigo A.; Santana, W. M.

doi:10.1142/s0218127408021282

Cited by 4 publications

(29 citation statements)

References 28 publications

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“…We conjecture that the boundary between the basins of attraction of the blue and red pre-crisis attractors is fractal. It is a known fact in dynamical systems that fractal basin boundaries can be formed by the stable manifold of a chaotic saddle (Battelino et al 1988;Rempel et al 2008). At the merging crisis, both attractors simultaneously collide with the chaotic saddle and its stable manifold at the basin boundary and the three sets (two attractors and a chaotic saddle) merge to form the post-crisis chaotic attractor.…”

Section: Formation Of a Chaotic Saddlementioning

confidence: 99%

“…Chaotic saddles may emerge in various manners, such as by the occurrence of a boundary crisis (Grebogi, Ott & Yorke 1983;Grebogi et al 1987), where a chaotic attractor collides with a fixed point or periodic orbit. Chaotic saddles can also be observed in relation to interior crises and fractal basin boundaries (Robert et al 2000;Rempel et al 2004Rempel et al , 2008.…”

Section: Appendix B Analysis Of the Chaotic Saddlementioning

confidence: 99%

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Transition to chaos in a reduced-order model of a shear layer

2021

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The present work studies the nonlinear dynamics of a shear layer, driven by a body force and confined between parallel walls, a simplified setting to study transitional and turbulent shear layers. It was introduced by Nogueira & Cavalieri (J. Fluid Mech., vol. 907, 2021, A32), and is here studied using a reduced-order model based on a Galerkin projection of the Navier–Stokes system. By considering a confined shear layer with free-slip boundary conditions on the walls, periodic boundary conditions in streamwise and spanwise directions may be used, simplifying the system and enabling the use of methods of dynamical systems theory. A basis of eight modes is used in the Galerkin projection, representing the mean flow, Kelvin–Helmholtz vortices, rolls, streaks and oblique waves, structures observed in the cited work, and also present in shear layers and jets. A dynamical system is obtained, and its transition to chaos is studied. Increasing Reynolds number $Re$ leads to pitchfork and Hopf bifurcations, and the latter leads to a limit cycle with amplitude modulation of vortices, as in the direct numerical simulations by Nogueira & Cavalieri. Further increase of $Re$ leads to the appearance of a chaotic saddle, followed by the emergence of quasi-periodic and chaotic attractors. The chaotic attractors suffer a merging crisis for higher $Re$ , leading to a chaotic dynamics with amplitude modulation and phase jumps of vortices. This is reminiscent of observations of coherent structures in turbulent jets, suggesting that the model represents a dynamics consistent with features of shear layers and jets.

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Section: Formation Of a Chaotic Saddlementioning

confidence: 99%

Section: Appendix B Analysis Of the Chaotic Saddlementioning

confidence: 99%

Transition to chaos in a reduced-order model of a shear layer

2021

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“…The effects of noise on Alfvén chaos were investigated by Rempel et al (2006Rempel et al ( , 2008. By adding a Gaussian noise to the stationary solutions of the DNLS, Rempel et al (2006) studied the occurrence of extrinsic transients and attractor hopping in a multistable regime of Alfvén waves.…”

Section: Alfvén Chaosmentioning

confidence: 99%

“…By adding a Gaussian noise to the stationary solutions of the DNLS, Rempel et al (2006) studied the occurrence of extrinsic transients and attractor hopping in a multistable regime of Alfvén waves. The complex dynamics of Alfvén waves described by DNLS was studied by Rempel et al (2008) when a nonlinear Alfvén wave is driven towards an intermittent regime by the addition of noise. The effects of Gaussian and non-Gaussian noise were compared.…”

Section: Alfvén Chaosmentioning

confidence: 99%

“…The aforementioned studies on Alfvén chaos elucidate how Alfvén intermittency appears in space and astrophysical plasmas, such as the magnetic intermittent turbulence observed in the solar wind (Koga et al, 2007;Sahraoui, 2008;Chian and Miranda, 2009;Chian and Muñoz, 2011), due to nonlinear dynamical phenomena such as the type-I intermittency induced by a saddle-node bifurcation, the crisisinduced intermittency induced by an interior crisis, and the extrinsic intermittency induced by a noise (Hada et al, 1990;Chian et al, 1998Chian et al, , 2006Chian et al, , 2007Rempel et al, 2006Rempel et al, , 2008Sánchez-Arriaga et al, 2009;Miranda et al, 2012).…”

Section: Jatenco-pereira Et Al: Alfvén Waves In Dusty Plasmasmentioning

confidence: 99%

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Alfvén waves in space and astrophysical dusty plasmas

Jatenco‐Pereira¹,

Chian

Rubab

2014

Nonlin. Processes Geophys.

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Abstract. In this paper, we present some results of previous works on Alfvén waves in a dusty plasma in different astrophysical and space regions by taking into account the effect of superthermal particles on the dispersive characteristics. We show that the presence of dust and superthermal particles sensibly modify the dispersion of Alfvén waves. The competition between different damping processes of kinetic Alfvén waves and Alfvén cyclotron waves is analyzed. The nonlinear evolution of Alfvén waves to chaos is reviewed. Finally, we discuss some applications of Alfvén waves in the auroral region of space plasmas, as well as stellar winds and star-forming regions of astrophysical plasmas.

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Nonlinear dynamics in space plasma turbulence: temporal stochastic chaos

Chian

Borotto

Hada

et al. 2022

Rev. Mod. Plasma Phys.

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Intermittent turbulence is key for understanding the stochastic nonlinear dynamics of space, astrophysical, and laboratory plasmas. We review the theory of deterministic and stochastic temporal chaos in plasmas and discuss its link to intermittent turbulence observed in space plasmas. First, we discuss the theory of chaos, intermittency, and complexity for nonlinear Alfvén waves, and parametric decay and modulational wave–wave interactions, in the absence/presence of noise. The transition from order to chaos is studied using the bifurcation diagram. The following two types of deterministic intermittent chaos in plasmas are considered: type-I Pomeau–Manneville intermittency and crisis-induced intermittency. The role of structures known as chaotic saddles in deterministic and stochastic chaos in plasmas is investigated. Alfvén complexity associated with noise-induced intermittency, in the presence of multistability, is studied. Next, we present evidence of magnetic reconnection and intermittent magnetic turbulence in coronal mass ejections in the solar corona and solar wind via remote and in situ observations. The signatures of turbulent magnetic reconnection, i.e., bifurcated current sheet, reconnecting jet, parallel/anti-parallel Alfvénic waves, and spiky dynamical pressure pulse, as well as fully developed turbulence, are detected at the leading edge of an interplanetary coronal mass ejection and the interface region of two merging interplanetary magnetic flux ropes. Methods for quantifying the degree of coherence, amplitude–phase synchronization, and multifractality of nonlinear multiscale fluctuations are discussed. The stochastic chaotic nature of Alfvénic intermittent structures driven by magnetic reconnection is determined by a complexity–entropy analysis. Finally, we discuss the relation of nonlinear dynamics and intermittent turbulence in space plasmas to similar phenomena observed in astrophysical and laboratory plasmas, e.g., coronal mass ejections and flares in the stellar-exoplanetary environment and Galactic Center, as well as chaos, magnetic reconnection, and intermittent turbulence in laser-plasma and nuclear fusion experiments.

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Alfvén Complexity

Cited by 4 publications

References 28 publications

Transition to chaos in a reduced-order model of a shear layer

Transition to chaos in a reduced-order model of a shear layer

Alfvén waves in space and astrophysical dusty plasmas

Nonlinear dynamics in space plasma turbulence: temporal stochastic chaos

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