differential model for 2d turbulence
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
Talk by S. Nazarenko, July 18, 2006
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
Leith’68 model of 3D turbulence
Kolmogorov solution:
Thermodynamic energy equipartition:
Talk by S. Nazarenko, July 18, 2006
“Warm” cascade
Analytical solution with both cascade and thermodynamic components, Connaugton & Nazarenko’2004.
Describes the bottleneck phenomenon.
Talk by S. Nazarenko, July 18, 2006
“warm cascade” (Connaughton, Nazarenko, 2004)
Cascade scaling at low k Thermodynamic at large k
Talk by S. Nazarenko, July 18, 2006
“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
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
Talk by S. Nazarenko, July 18, 2006
Talk by S. Nazarenko, July 18, 2006
Talk by S. Nazarenko, July 18, 2006
Talk by S. Nazarenko, July 18, 2006
Talk by S. Nazarenko, July 18, 2006
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
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
Differential model for 2D turbulence (DM2D)
Lvov and Nazarenko’2006.
Talk by S. Nazarenko, July 18, 2006
Invariants of DM2D
Talk by S. Nazarenko, July 18, 2006
Energy and Enstrophy Fluxes
Talk by S. Nazarenko, July 18, 2006
Cascade solutions
Talk by S. Nazarenko, July 18, 2006
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
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
Nastrom-Gage spectrum
Nastrom & Gage’84,
Friction?Gkioulekas’0
5
Talk by S. Nazarenko, July 18, 2006
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
Direct cascade with friction
Talk by S. Nazarenko, July 18, 2006
Inverse cascade with friction
Talk by S. Nazarenko, July 18, 2006
Summary of friction effects
There is no Nastrom-Gage shape Friction arrests both cascades at finite scales.
Talk by S. Nazarenko, July 18, 2006
Lilly’89 model Get rid of the thermodynamic
solutions – 2nd order equation:
NG spectrum, Lilly’89
Talk by S. Nazarenko, July 18, 2006
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.