Phase dynamics of alfven intermittent turbulence in the heliosphere
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Phase Dynamics of Alfven Intermittent Turbulence in the Heliosphere. Abraham C.-L. Chian National Institute for Space Research (INPE), Brazil & Erico L. Rempel, ITA, Brazil. Outline. Observation of Alfven intermittent turbulence in the heliosphere

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Phase Dynamics of Alfven Intermittent Turbulence in the Heliosphere

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Phase Dynamics of Alfven Intermittent Turbulence in the Heliosphere

Abraham C.-L. Chian

National Institute for Space Research (INPE), Brazil

&

Erico L. Rempel, ITA, Brazil


Outline

  • Observation of Alfven intermittent turbulence in the heliosphere

  • Model of nonlinear phase dynamics of Alfven intermittent turbulence


Observation of Alfven intermittent turbulence

in the heliosphere


Intermittency

  • Time series displays random regime switching between laminar and bursty periods of fluctuations

  • Probability distribution function (PDF) displays a non-Gaussian shape due to large-amplitude fluctuations at small scales

  • Power spectrum displays a power-law behavior

    Ref.:

    Burlaga, Interplanetary Magnetohydrodynamics, Oxford U. P. (1995)

    Biskamp, Magnetohydrodynamic Turbulence, Cambridge U. P. (2003)

    Lui, Kamide & Consolini, Multiscale Coupling of Sun-Earth Processes,

    Elsevier (2005)


Alfvén intermittency in the solar wind

  • Time evolution of velocity fluctuations measured by

    Helios 2, V() = V(t+)-V(t), at 4 different time scales ():

  • Carbone et al., Solar Wind X, 2003


Non-Gaussian PDF for Alfven intermittency in the solar wind measured by Helios 2

Slow streams

Fast streams

dbt = B(t + t) – B(t)

  • Sorriso-Valvo et al., PSS, 49, 1193 (2001)


Power-law behavior in the power spectrum of Alfvén intermittency in high-speed solar wind

Power spectra of outward (solid lines) and inward (dotted lines) propagating Alfvénic fluctuations in high-speed solar wind, indicating power-law behavior

  • Helios spacecraft (Marsch & Tu, 1990)


Chaos

Chaotic Attractors and Chaotic Saddles:

  • Sensitive dependence on initial conditions and system parameters

  • Aperiodic behavior

  • Unstable periodic orbits

    Ref:

    Lorenz, J. Atm. Sci. (1963) => Lorenz chaotic attractor

    Chian, Kamide, et al., JGR (2006)=> Alfven chaotic saddle


Evidence of chaos in the heliosphere

  • Chaos in Alfven turbulence in the solar wind

    Macek & Radaelli, PSS (2001)

    Macek et al., PRE (2005)

  • Chaos in solar radio emissions

    Kurths & Karlicky, SP (1989)

    Kurths & Schwarz, SSRv (1994)

  • Chaos in the (AE, AL) auroral indices

    Vassialiadis et al., GRL (1990)

    Sharma et al., GRL (1993)

    Pavlos et al., NPG (1999)


Unstable periodic orbits and turbulence

  • Spatiotemporal chaos can be described in terms of UPOs

  • Christiansen et al., Nonlinearity 1997

  • Identification of an UPO in plasma turbulence in a tokamak experiment

  • Bak et al, PRL 1999

  • Sensitivity of chaotic attractor of a barotropic ocean model to external

  • influences can be described by UPOs

  • Kazantsev, NPG, 2001

  • Intermittency of a shell model of fluid turbulence is described by an UPO

  • Kato and Yamada, Phys. Rev. 2003

  • Control of chaos in a fluid turbulence by stabilization of an UPO

  • Kawahara, Phys. Fluids 2005


Model of nonlinear phase dynamics of

Alfven intermittent turbulence


Phase dynamics of MHD turbulence in the solar wind

  • Geotail magnetic field data shows evidence of phase coherence in MHD waves in the solar wind

  • Hada, Koga and Yamamoto, SSRv 2003

  • Phase coherence of MHD turbulence upstream of the Earth’s bow shock

  • Koga and Hada, SSRv 2003


Two approaches to Alfven chaos

  • Low-dimensional chaos:

    Stationary solutions of the derivative nonlinear Schroedinger equation

    Hada et al., Phys. Fluids 1990

    Rempel and Chian, Adv. Space Res. 2005

    Chian et al., JGR 2006

  • High-dimensional chaos:

    Spatiotemporal solutions of the Kuramoto-Sivashinsky equation

    Chian et al., Phys. Rev. E 2002

    Rempel et al., Nonlinear Proc. Geophys. 2005

    Rempel and Chian, Phys. Rev. E 2005


Kuramoto-Sivashinsky equation

Phase dynamics of a NL Alfven wave is governed by the Kuramoto-Sivashinsky eqn.

(LaQuey et al. PRL 1975, Chian et al. PRE 2002, Rempel and Chian PRE 2005):

  • is a damping parameter.

    Assuming periodic boundary conditions: (x,t) = (x+2,t) and expanding  in a Fourier series:

we obtain a set of ODE’s for the Fourier modes ak:

We seek odd solutions by assuming ak purely imaginary


Spatiotemporal phase dynamics of Alfven waves

Truncation: N = 16 Fourier modes

  • Chian et al., PRE (2002)

  • Rempel and Chian, Phys. Lett. A (2003)

  • Rempel et al., NPG (2005)

  • Rempel and Chian, PRE (2005)


Chaotic solutions

  • Chaotic Attractors:

    - Set of unstable periodic orbits

    - Positive maximum Lyapunov exponent

    • Attract all initial conditions in a given neighbourhood

      (basin of attraction)

    • Responsible for asymptotic chaos

  • Chaotic Saddles (Chaotic Non-Attractors):

    • Set of unstable periodic orbits

    • Positive maximum Lyapunov exponent

    • Repel most initial conditions from their neighbourhood, except those on stable manifolds

      (no basin of attraction)

    • Responsible for transient chaos


Bifurcation Diagram

  • Rempel and Chian, PRE 71, 016203 (2005).


Attractor Merging Crisis


Post-Crisis Chaotic Saddles

Rempel and Chian, PRE 71, 016203 (2005)


Crisis-induced intermittency

n = 0.02990

Rempel and Chian, PRE 71, 016203 (2005)


Characteristic intermittency time

Rempel and Chian, PRE 71, 016203 (2005)


BS

HILDCAA(High Intensity Long Duration Continuous Auroral Activities)

  • IMP 8

  • Gonzalez, Tsurutani, Gonzalez, SSR 1999

  • Tsurutani, Gonzalez, Guarnieri, Kamide, Zhou, Arballo, JASTP (2004)


CONCLUSIONS

  • Observational evidence of chaos and intermittency in the heliosphere

  • Dynamical systems approach provides a powerfull tool to probe the complex nature of space environment, e.g., Alfven intermittent turbulence

  • Unstable structures (unstable periodic orbits and chaotic saddles) are the origin of intermittent turbulence

  • Characteristic intermittency time can be useful for space weather and space climate forecasting


Advanced School on Space Environment (ASSE 2006)10-16 September 2006, L’Aquila – ItalyConveners: R. Bruno, A. Chian, Y. Kamide, U. VillanteHandbook of Solar-Terrestrial EnvironmentEditors: Y. Kamide and A. ChianSpringer 2006

WISER mission:

‘linking nations for the peaceful use of the earth-ocean-space environment’

(www.cea.inpe.br/wiser)


THANK YOU !


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