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Modeling the Intermittent Dynamics of Alfvén Waves in the Solar Wind

Modeling the Intermittent Dynamics of Alfvén Waves in the Solar Wind. Abraham C.-L. Chian National Institute for Space Research (INPE), Brazil & Yohsuke Kamide (Nagoya U., Japan), Erico L. Rempel (ITA, Brazil), Wanderson M. Santana (INPE, Brazil). Outline.

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Modeling the Intermittent Dynamics of Alfvén Waves in the Solar Wind

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  1. Modeling the Intermittent Dynamics of Alfvén Waves in the Solar Wind Abraham C.-L. Chian National Institute for Space Research (INPE), Brazil & Yohsuke Kamide (Nagoya U., Japan), Erico L. Rempel (ITA, Brazil), Wanderson M. Santana (INPE, Brazil)

  2. Outline • Relevance of intermittency and chaos in the solar-terrestrial environment • Modeling the interplanetary Alfvén intermittency driven by chaos Ref: Chian et al., On the chaotic nature of solar-terrestrial environment: interplanetary Alfvén intermittency, JGR 2006

  3. 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 an excess of large- and small-amplitude fluctuations at small scales • Power spectrum displays a power-law behavior

  4. Evidence of intermittency in the solar-terrestrial environment • Alfvén intermittency in the solar wind Bruno et al., ASR (2005) Bruno & Carbone, http://solarphysics.livingreviews.org (2005) • Intermittency in the Auroral Electrojet (AE) index Consolini & De Michelis, GRL (1998, 2005) • Intermittency in the earth´s plasma sheet related to bursty bulk flows in the magnetotail Angelopoulos, Mukai & Kokubun, PP (1999); Voros et al., JGR (2004)

  5. 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

  6. 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)

  7. 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)

  8. Chaos Chaotic Attractors & Chaotic Saddles: • Sensitive dependence on initial conditions and system parameters • Aperiodic behavior • Unstable periodic orbits Lorenz, J. Atm. Sci. (1963): Lorenz chaotic attractor => Weather / Climate Chian et al., JGR (2006):Alfvén chaotic saddle => Space Weather / Space Climate

  9. Chaotic sets • Chaotic Attractors: - Set of unstable periodic orbits • Positive maximum Lyapunov exponent - Attract all initial conditions in a given neighbourhood - Basin of attraction (continuous stable manifolds, without gaps) - Responsible for asymptotic chaos • Chaotic Saddles: - 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 (fractal stable manifolds, with gaps) - Responsible for transient chaos

  10. Evidence of chaos in the solar-terrestrial environment • Chaos in Alfvén 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 Baker et al., GRL (1990) Sharma et al., GRL (1993) Pavlos et al., NPG (1999)

  11. Derivative nonlinear Schrodinger equation Large-amplitude Alfvén wave propagating along the ambient magnetic field in the x direction: b = by+ibz • = dissipation a = 1/[4(1-)],  = c2S / c2A,  = dispersion • S(b,x,t) = Aexp(ik): a circularly-polarized driver wave •  = x - Vt

  12. Bifucation diagram: global view

  13. Bifurcation diagram: periodic window

  14. Unstable periodic orbits

  15. Interior Crisis:pre- and post-crisis

  16. M Coupling unstable periodic orbit (p-11 UPO)

  17. Alfvén crisis-induced intermittency

  18. Characteristic intermittency time

  19. BS HILDCAA(High Intensity Long Duration Continuous Auroral Activities) • IMP 8 • Gonzalez, Tsurutani, Gonzalez, SSR 1999 • Tsurutani, Gonzalez, Guarnieri, Kamide, Zhou, Arballo, JASTP (2004)

  20. CONCLUSIONS • Observational evidence of chaos and intermittency in the • Sun-Earth system • Dynamical systems approach provides a powerfull tool to probe the complex nature of solar-terrestrial environment, e.g., • Alfvén intermittent turbulence in the solar wind • 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

  21. Books • Handbook of Solar-Terrestrial Environment • Y. Kamide and A.C.-L. Chian (Eds.) • Springer, 2006 • (ASSE 2006) • Fundamentals of Space Environment Science • V. Jatenco, A. C.-L Chian, J. F. Valdes and M.A. Shea (Eds.) • Elsevier, 2005 • (ASSE 2004) • Advances in Space Environment Research • A.C.-L. Chian and the WISER Team (Eds.) • Kluwer, 2003 • (WSEF 2002, HPC 2002) • Complex Systems Approach to Economic Dynamics • A.C.-L. Chian • Springer, 2006 WISER mission: ‘linking nations for the peaceful use of the earth-ocean-space environment’ (www.cea.inpe.br/wiser)

  22. THANK YOU !

  23. Two approaches to dynamical systems • Low-dimensional chaos: Stationary solutions of the derivative nonlinear Schroedinger equation Hada et al., Phys. Fluids 1990 Chian et al., ApJ 1998 Borotto et al., Physica D 2004 Rempel et al., Phys. Plasmas 2006 Chian et al., JGR 2006 • High-dimensional chaos: Spatiotemporal solutions of the Kuramoto-Sivashinsky equation and the regularized long-wave equation Chian et al., Phys. Rev. E 2002 He and Chian, Phys. Rev. Lett. 2003 He and Chian, Phy. Rev. E 2004 Rempel and Chian, Phys. Rev. E 2005

  24. Unstable periodic orbits & turbulence • UPOS in the Kuramoto-Sivashinsky equation • Christiansen et al., Nonlinearity 1997; Zoldi and Greenside, PRE 1998 • 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 and Kida, J. Fluid Mech. 2001; Kawahara, Phys. Fluids 2005

  25. Chaotic saddles & turbulence • Supertransient in the complex Ginzburg-Landau equation • Braun and Feudel, PRE 1996 • Detecting and computing chaotic sadddles in higher dimensions • Sweet, Nusse and Yorke, PRL 1996 • Close to the transition from laminar to turbulent flows the turbulent state corresponds to a chaotic saddle • Eckhardt and Mersmann, PRE 1999 • Chemical and biological activity in open flows • Tél et al, Phys. Rep. 2005 • Dispersion of finite-size particles in open chaotic advection • Vilela, de Moura and Grebogi, PRE 2006 • Edge of chaos in a parallel shear flow • Skufca, Yorke and Eckhardt, PRL 2006

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