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

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Presentation on theme: "Risø, ETH, Tel Aviv Uni Acceleration structure in turbulence Beat Lüthi, Alex Liberzon, Markus Holzner, Arkady Tsinober, Søren Ott, Jacob Berg, Jakob Mann."— Presentation transcript:

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 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


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