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Differential Model for 2D Turbulence

Differential Model for 2D Turbulence. Sergey Nazarenko, Warwick, UK In collaboration with Victor Lvov, Weizmann JETP Letters, 2006, Vol. 83, No. 12, pp. 541–545. Leith’68 model of 3D turbulence. Kolmogorov solution:. Thermodynamic energy equipartition:. “Warm” cascade.

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Differential Model for 2D Turbulence

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  1. Differential Model for 2D Turbulence Sergey Nazarenko, Warwick, UK In collaboration with Victor Lvov, Weizmann JETP Letters, 2006, Vol. 83, No. 12, pp. 541–545. Talk by S. Nazarenko, July 18, 2006

  2. Leith’68 model of 3D turbulence Kolmogorov solution: Thermodynamic energy equipartition: Talk by S. Nazarenko, July 18, 2006

  3. “Warm” cascade • Analytical solution with both cascade and thermodynamic components, Connaugton & Nazarenko’2004. • Describes the bottleneck phenomenon. Talk by S. Nazarenko, July 18, 2006

  4. “warm cascade” (Connaughton, Nazarenko, 2004) • Cascade scaling at low k • Thermodynamic at large k Talk by S. Nazarenko, July 18, 2006

  5. “gelation” and anomalous wake • Self-similar solution reaching infinite k in finite time • Spectrum in the wake is steeper than Kolmogorov Talk by S. Nazarenko, July 18, 2006

  6. Setup of Kolmogorov • After reaching infinite k, the Kolmogorov spectrum sets up as a reflected from infinity wave • Typical for all finite capacity spectra • Previously seen in Weak MHD turbulence (Galtier, Nazarenko, Newell, Pouquet, 2000) Talk by S. Nazarenko, July 18, 2006

  7. Talk by S. Nazarenko, July 18, 2006

  8. Talk by S. Nazarenko, July 18, 2006

  9. Talk by S. Nazarenko, July 18, 2006

  10. Talk by S. Nazarenko, July 18, 2006

  11. Talk by S. Nazarenko, July 18, 2006

  12. Superfluid turbulence Turbulent superfluid and normal components coupled via mutual friction,Lvov, Nazarenko, Volovik’2005; Vinen 2005; Lvov, Nazarenko, Skrbek’2006. Talk by S. Nazarenko, July 18, 2006

  13. Systems with dual cascades Gravity wave turbulence on water surface,Hasselmann & Hasselmann’85;Dyachenko, Newell, Pushkarev, Zakharov’91 Talk by S. Nazarenko, July 18, 2006

  14. Differential model for 2D turbulence (DM2D) • Lvov and Nazarenko’2006. Talk by S. Nazarenko, July 18, 2006

  15. Invariants of DM2D Talk by S. Nazarenko, July 18, 2006

  16. Energy and Enstrophy Fluxes Talk by S. Nazarenko, July 18, 2006

  17. Cascade solutions Talk by S. Nazarenko, July 18, 2006

  18. Predictions for Kolmogorov constants • Ihihara & Kaneda’2001; Danilov & Gurarie’2001 DNS: CQ/CP=1.9/6=0.32 Lvov, Pomyalov, Proccacia’2002 Talk by S. Nazarenko, July 18, 2006

  19. Effect of friction • Change of scaling like in superfluids? • Change of scaling due to friction in passive scalar (Chertkov’98) and 2D turbulence Boffetta et al’2005) Talk by S. Nazarenko, July 18, 2006

  20. Nastrom-Gage spectrum Nastrom & Gage’84, Friction? Gkioulekas’05 Talk by S. Nazarenko, July 18, 2006

  21. Not here… • Now, the -3 exponent is in resonance with the inverse cascade exponent. • Hence a log rather than power-law correction. Talk by S. Nazarenko, July 18, 2006

  22. Direct cascade with friction Talk by S. Nazarenko, July 18, 2006

  23. Inverse cascade with friction Talk by S. Nazarenko, July 18, 2006

  24. Summary of friction effects • There is no Nastrom-Gage shape • Friction arrests both cascades at finite scales. Talk by S. Nazarenko, July 18, 2006

  25. Lilly’89 model • Get rid of the thermodynamic solutions – 2nd order equation: NG spectrum, Lilly’89 Talk by S. Nazarenko, July 18, 2006

  26. Summary • Differential models: put something in in order to get more useful stuff out. • Time evolution. Setup of cascades. Rate of total energy and enstrophy decay. • Mixed solutions with simultaneous cascades and thermal components. • Friction effects and other modifications. Talk by S. Nazarenko, July 18, 2006

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