Acceleration structure in turbulence

Risø, ETH, Tel Aviv Uni

Acceleration structure in turbulence

Beat Lüthi, Alex Liberzon, Markus Holzner, Arkady Tsinober,

Søren Ott, Jacob Berg, Jakob Mann

Oct 2009EUROMECH Colloquium 512, Torino

Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 2/23


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




Introduction

acceleration coupled to small scales, i.e. velocity gradients




Introduction

but also coupled to large scales




High magnitude in strain and/or enstrophy?

larger than unity,but decreasing with Re




High Re – low Re is qualitatively the same for acceleration structure

Re= 70Re= 6600




Particle Tracking Velocimetry, 3d-PTV





Cam

era

4C

amer

a 3

Cam

era

1C

amer

a 2

x

yz

r(x,y,z,t)








Aij from 3d-PTV




Accuracy?




Accuracy?




Accuracy?




Accuracy?Nature 2003:




Acceleration magnitude




Acceleration magnitude

three distinct regions




Curvature

no correspondence between strong curvature and strong vorticity

strong curvature is highly correlated with low velocityright tail of PDF scales with -5/2




weak separation upon conditioningon high strain and enstrophy

Curvature

adding velocity results inscaling change from -5/2 to -7/2

streamline curvaturescales with -11/2

stronger separation withhigh strain and enstrophy




Curvaturewhy seemingly enstrophy dominated?al ac cancelation in high strain is low Re effect




Geometrical structure




Geometrical structure

1

3ω

ac




Velocity acceleration structure function




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

Documents

Acceleration structure in turbulence