1. Risø, ETH, Tel Aviv Uni Acceleration structure in turbulence Beat Lüthi, Alex Liberzon, Markus Holzner, Arkady Tsinober, Søren Ott, Jacob Berg, Jakob Mann

2. Oct 2009 EUROMECH Colloquium 512, Torino Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 2/23 Risø, ETH, Tel Aviv Uni Aim of talk  gain inisght also in spatial structure (not just magnitude)  strong acceleration in high strain and high enstrophy  for low Re curvature mainly in high enstrophy  for high Re curvature in high strain and high enstrophy  geometrical alignments of acceleration quantities  velocity-acceleration struct. func. and energy flux

3. Oct 2009 EUROMECH Colloquium 512, Torino Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 3/23 Risø, ETH, Tel Aviv Uni Introduction  acceleration coupled to small scales, i.e. velocity gradients

4. Oct 2009 EUROMECH Colloquium 512, Torino Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 4/23 Risø, ETH, Tel Aviv Uni Introduction  but also coupled to large scales

5. Oct 2009 EUROMECH Colloquium 512, Torino Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 5/23 Risø, ETH, Tel Aviv Uni High magnitude in strain and/or enstrophy? larger than unity, but decreasing with Re

6. Oct 2009 EUROMECH Colloquium 512, Torino Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 6/23 Risø, ETH, Tel Aviv Uni High Re – low Re is qualitatively the same for acceleration structure Re = 70 Re = 6600

7. Oct 2009 EUROMECH Colloquium 512, Torino Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 7/23 Risø, ETH, Tel Aviv Uni Particle Tracking Velocimetry, 3d-PTV

8. Oct 2009 EUROMECH Colloquium 512, Torino Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 8/23 Risø, ETH, Tel Aviv Uni Particle Tracking Velocimetry, 3d-PTV Camera 4 Camera 3 Camera 1 Camera 2 x y z r(x,y,z,t)

9. Oct 2009 EUROMECH Colloquium 512, Torino Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 9/23 Risø, ETH, Tel Aviv Uni Particle Tracking Velocimetry, 3d-PTV

10. Oct 2009 EUROMECH Colloquium 512, Torino Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 10/23 Risø, ETH, Tel Aviv Uni A ij from 3d-PTV

11. Oct 2009 EUROMECH Colloquium 512, Torino Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 11/23 Risø, ETH, Tel Aviv Uni Accuracy?

12. Oct 2009 EUROMECH Colloquium 512, Torino Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 12/23 Risø, ETH, Tel Aviv Uni Accuracy?

13. Oct 2009 EUROMECH Colloquium 512, Torino Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 13/23 Risø, ETH, Tel Aviv Uni Accuracy?

14. Oct 2009 EUROMECH Colloquium 512, Torino Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 14/23 Risø, ETH, Tel Aviv Uni Accuracy? Nature 2003:

15. Oct 2009 EUROMECH Colloquium 512, Torino Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 15/23 Risø, ETH, Tel Aviv Uni Acceleration magnitude

16. Oct 2009 EUROMECH Colloquium 512, Torino Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 16/23 Risø, ETH, Tel Aviv Uni Acceleration magnitude three distinct regions

17. Oct 2009 EUROMECH Colloquium 512, Torino Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 17/23 Risø, ETH, Tel Aviv Uni Curvature no correspondence between strong curvature and strong vorticity strong curvature is highly correlated with low velocity right tail of PDF scales with -5/2

18. Oct 2009 EUROMECH Colloquium 512, Torino Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 18/23 Risø, ETH, Tel Aviv Uni weak separation upon conditioning on high strain and enstrophy Curvature adding velocity results in scaling change from -5/2 to -7/2 streamline curvature scales with -11/2 stronger separation with high strain and enstrophy

19. Oct 2009 EUROMECH Colloquium 512, Torino Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 19/23 Risø, ETH, Tel Aviv Uni Curvature why seemingly enstrophy dominated?a l a c cancelation in high strain is low Re effect

20. Oct 2009 EUROMECH Colloquium 512, Torino Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 20/23 Risø, ETH, Tel Aviv Uni Geometrical structure

21. Oct 2009 EUROMECH Colloquium 512, Torino Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 21/23 Risø, ETH, Tel Aviv Uni Geometrical structure 1 3 ω acac

22. Oct 2009 EUROMECH Colloquium 512, Torino Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 22/23 Risø, ETH, Tel Aviv Uni Velocity acceleration structure function

23. Oct 2009 EUROMECH Colloquium 512, Torino Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 23/23 Risø, ETH, Tel Aviv Uni Conclusions  high acceleration magnitude also in high strain regions  curvature scales with -7/2 not with -5/2 if Re is very high  identify reason why @ low Re curvature correlates with vorticity, but why this effects vanishes for high Re  alignment with eigenframe stronger for a c, associated with stream lines  alignments are of kinematical nature  From vel-acc struct function we arrive at similar result for energy flux as Leonard, 1974, Borue&Orzag 1998