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Insights into Acceleration Structures in Turbulent Flows

This talk explores the intricate acceleration structures within turbulent flows, focusing on the spatial arrangement of accelerations and their relationship to strain and enstrophy. We discuss significant findings, including the behavior of acceleration in both low and high Reynolds numbers, and its correlation with velocity gradients and curvature. Our research utilizes advanced Particle Tracking Velocimetry (3D-PTV) to examine these dynamics, revealing critical insights into energy flux and geometrical alignments that govern turbulence.

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Insights into Acceleration Structures in Turbulent Flows

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

  2. 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. Introduction • acceleration coupled to small scales, i.e. velocity gradients

  4. Introduction • but also coupled to large scales

  5. larger than unity, but decreasing with Re High magnitude in strain and/or enstrophy?

  6. Rel= 70 Rel= 6600 High Re – low Re is qualitatively the same for acceleration structure

  7. Particle Tracking Velocimetry, 3d-PTV

  8. r(x,y,z,t) Camera 4 Camera 1 z y Camera 3 Camera 2 x Particle Tracking Velocimetry, 3d-PTV

  9. Particle Tracking Velocimetry, 3d-PTV

  10. Aij from 3d-PTV

  11. Accuracy?

  12. Accuracy?

  13. Accuracy?

  14. Accuracy? Nature 2003:

  15. Acceleration magnitude

  16. three distinct regions Acceleration magnitude

  17. no correspondence between strong curvature and strong vorticity strong curvature is highly correlated with low velocity right tail of PDF scales with -5/2 Curvature

  18. streamline curvature scales with -11/2 stronger separation with high strain and enstrophy weak separation upon conditioning on high strain and enstrophy adding velocity results in scaling change from -5/2 to -7/2 Curvature

  19. Curvature al ac cancelation in high strain is low Re effect why seemingly enstrophy dominated?

  20. Geometrical structure

  21. l1 l3 ω ac Geometrical structure

  22. Velocity acceleration structure function

  23. 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 ac, 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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