| 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 |