Feedback Loop in 2D: Formation of Zonal Jets and Suppression of Turbulence

Sergey Nazarenko, Warwick, UK
Drift waves in fusion devices
Charney-Hasegawa-Mima equation
Baroclinic instability and ITG
Low-to-High confinement transitions in fusion plasmas
LH transition paradigm
Barotropic governor in GFG
Zonal flow generation:
the local turbulence view.
Ubiquitous features in Drift/Rossby turbulence
Rhines scale crossover
Weakly nonlinear drift waves with random phases→ wave kinetic equation (Longuet-Higgens &Gill, 1967)
Anisotropic cascades in drift turbulence
Cartoon of nonlocal interaction
Small-scale energy conservation
Nonlocal 2D turbulence
Condensate coupled with turbulence
Feedback loop in 2D turbulence
Modulational Instability
Manin, Nazarenko, 1994; Manfroi, Young, 1999;
 Smolyakov et al, 2000;
Ongoing numerics: Connaughton, Nadiga, SN, Quinn.
Nonlinear development of MI:
narrow zonal jets
Evolution in the k-space
Fast mode: modulational instability of a coherent drift wave.
Evolution of nonlocal drift turbulence:
retain only interaction with small kÕs and Taylor-expand the integrand of the wave-collision integral; integrate.
Drift-Wave instabilities
Initial evolution
ZF growth
ZF growth
Steady state
Shats experiment
Shats experiment
Saturation of zonal flow
Summary
Breakdown of local cascades
Coupled large-scale & small-scale  motions
(Dyachenko, Nazarenko, Zakharov, 1992)
Shear flow geometry
"North-Pacific zonal jets at 1000..."
Co-authors and relevant publications
Ubiquitous features in Drift/Rossby turbulence
Drift wave – zonal flow turbulence paradigm
Zonostrophy invariant
"At high kÕs it is..."
Plan