Detection of drift-kinetic vortices as a manifestation of Alfvénic turbulence

D. Sundkvist†,

†IRF, Uppsala, Sweden

LPCE/CNRS, Orléans, France

Dep. Astronomy and Space Physics, UU, Sweden

Outline

Phenomenology of turbulence

MHD turbulence in the solar wind

Turbulence in the polar cusp

Drift-wave turbulence and coherent structures

Analytical solution of drift-kinetic Alfvén vortices

In situ detection of drift-kinetic electromagnetic vortices in the cusp close to dissipation scale

Leonardo and la turbolenza

“Observe the motion of the surface of the water, which

resembles that of hair, which has two motions, of which

one is caused by the weight of the hair, the other by the

direction of the curls; thus the water has eddying

motions, one part of which is due to the principal

current, the other to random and reverse motion.”

Leonardo da Vinci

1452-1519

First to try and scientifically study

turbulent phenomena

Phenomenology of turbulence

Turbulence is stochastic

detailed behaviour of turbulence cannot be predicted (?): resort to averages, correlation functions and probability density functions

Turbulence needs to be fed with energy

without an energy source the turbulence state decays to a laminar state

Turbulence is scale free

in the inertial range all scales are equal

Interactions are mediated by waves and eddies

observations in fluids and simulations show formation of coherent structures (vortices)

Dimensionless Reynolds number: Re=/VL=VL/

Richardson cascade Kolmogorov spectrum

Statistical and dimensional arguments based on Richardson's cascade picture

Assumptions: homogeneous, isotropic, incompressible turbulence

Turbulent (Richardson) cascade:

Energy goes from larger scales to smaller scales

General classical picture:

Energy fed at inertial range lo

Dissipationless transfer towards smaller scales in the inertial range

Dissipation into heat at the dissipation scale

Fluid turbulence is contained in the Navier-Stokes equation

MHD turbulence in the MHD equations

Magnetic field complicates the dynamics

In magnetized plasmas, the ambient magnetic field decouples || and ⊥ dynamics

MHD turbulence in the solar wind

Energy injection – solar wind (supersonic)

  5, vph = vA (Alfvénic)

Taylor's hypothesis (Doppler shift): kvsw

Kolmogorov spectrum with index = -5/3 (fluid like)

Dissipation scale, Alfvén waves --> Kinetic Alfvén waves

Kinetic Alfvén waves --> Heating?

Bale et al. Measurement of the Electric Fluctuation Spectrum of

Magnetohydrodynamic Turbulence, PRL, 94, 215002-1 (2005)

Turbulence in the polar cusp

High-altitude cusp

me/mi≪ ≪ 1

Strongly inhomogeneous

Kinetic Alfvén waves and ion cyclotron waves close to dissipation scale

MHD inadequate ---> Drift-wave Alfvénic turbulence

Sundkvist et al. Wave characteristics near proton

gyrofrequency in high-altitude cusp,

Ann. Geophys., 23, 983-995 (2005).

Goldstein Turbulence on a small scale, Nature, 436, 782 (2005).

Nykyri et al. Ion cyclotron waves in high altitude

cusp: CLUSTER observations at varying spacecraft

separations, GRL, 30, 2263 (2003).

Drift-wave turbulence and coherent structures

A model equation for low-frequency drift-wave plasma turbulence is the

Charney-Hasegawa-Mima (CHM) equation

The CHM-equation admit both wave and coherent (vortex) solutions

and is appropriate to describe low-frequency drift-wave turbulence

Horton & Hasegawa Quasi-two-dimensional dynamics of

plasmas and fluids, Chaos, 4, 227-251 (1994)

T.Taniuti

Generalization of CHM-equation

Can be derived from two-fluid equations:

For the parameters in the cusp we can assume

Momentum fluid equations lead to the drift velocities

which together with quasi-neutrality and the momentum and continuity equations gives the system

This system generalizes and reduce to CHM for Az =0, p = 0. The system describes both drift-Alfvén waves and vortices

Previous single-spacecraft observations of coherent structures

Chmyrev et al (1988) suggested that they observed drift-kinetic vortices in the plasma sheet boundary layer

To be sure one needs to separate temporal from spatial phenomena

Chmyrev et al. Alfvén vortices and related phenomena in the

Ionosphere and the Magnetosphere, Physica Scripta, 38,

841-854 (1988).

Multi-satellite detection of DKA vortices

Sundkvist et al. In Situ Multi-Satellite Detection of Coherent

Vortices as a Manifestation of Alfvenic Turbulence,

Nature, 436, 825-828 (2005).

Cusp crossing 2002-03-09

Northern outbound crossing

Northward IMF -> high-latitude reconnection

Turbulent boundary layer formed

Hodograms along trajectory suggest vortex motion

Cluster --> Multi-point measurements

Detection of DKA vortices – Multipoint timeseries analysis

New point of view: look for coherent structures by examining time-series from several spacecraft simultaneously

Rotation of field vectors spatially coherent

In accord with vortex convected past the spacecraft

Vortex radius approximately 2-6 p

Sundkvist et al. In Situ Multi-Satellite Detection of Coherent

Vortices as a Manifestation of Alfvenic Turbulence,

Nature, 436, 825-828 (2005).

Detection of DKA vortices – Comparison with theory

Sundkvist et al. In Situ Multi-Satellite Detection of Coherent

Vortices as a Manifestation of Alfvenic Turbulence,

Nature, 436, 825-828 (2005).

Sundkvist et al. Manuscript in preparation, J. Geophy. Res., (2005).

Model of vortex turbulence in cusp: isolated DKA vortices

In accord with observations

spectra

rotation of field vectors

Summary

High-altitude cusp boundary layer:

low beta (kinetic regime) drift-wave Alfvénic turbulence

Appropiate equations are generalizations of Charney-Hasegawa-Mima equation

Strong drift-turbulence: drift-waves and coherent vortices (owing to self-interaction among kinetic Alfvén waves via vector nonlinearities)

Analytical solutions exist: Drift-Kinetic electromagnetic Alfvén vortices (DKA vortices)

Multi-point measurements by Cluster four spacecraft confirms existence of small scale coherent structures (vortices)

Observations of coherent structures can be described as DKA vortices and vortex chains

2004-06-17T17:20:39