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

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

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

Observation of Alfven intermittent turbulence

in the heliosphere


Intermittency

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)


Alfv n intermittency in the solar wind

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

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 alfv n intermittency in high speed solar wind

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

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


Phase dynamics of alfven intermittent turbulence in the heliosphere

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

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

Model of nonlinear phase dynamics of

Alfven intermittent turbulence


Phase dynamics of mhd turbulence in the solar wind

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


Phase dynamics of alfven intermittent turbulence in the heliosphere

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

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


Phase dynamics of alfven intermittent turbulence in the heliosphere

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 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

Bifurcation Diagram

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


Attractor merging crisis

Attractor Merging Crisis


Post crisis chaotic saddles

Post-Crisis Chaotic Saddles

Rempel and Chian, PRE 71, 016203 (2005)


Crisis induced intermittency

Crisis-induced intermittency

n = 0.02990

Rempel and Chian, PRE 71, 016203 (2005)


Characteristic intermittency time

Characteristic intermittency time

Rempel and Chian, PRE 71, 016203 (2005)


Hildcaa high intensity long duration continuous auroral activities

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

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


Phase dynamics of alfven intermittent turbulence in the heliosphere

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

THANK YOU !


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