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
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
Oct 2009EUROMECH 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
Oct 2009EUROMECH 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
Oct 2009EUROMECH 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
Oct 2009EUROMECH 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= 70Re= 6600
Oct 2009EUROMECH Colloquium 512, Torino
Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 7/23
Risø, ETH, Tel Aviv Uni
Particle Tracking Velocimetry, 3d-PTV
Oct 2009EUROMECH Colloquium 512, Torino
Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 8/23
Risø, ETH, Tel Aviv Uni
Particle Tracking Velocimetry, 3d-PTV
Cam
era
4C
amer
a 3
Cam
era
1C
amer
a 2
x
yz
r(x,y,z,t)
Oct 2009EUROMECH Colloquium 512, Torino
Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 9/23
Risø, ETH, Tel Aviv Uni
Particle Tracking Velocimetry, 3d-PTV
Oct 2009EUROMECH Colloquium 512, Torino
Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 10/23
Risø, ETH, Tel Aviv Uni
Aij from 3d-PTV
Oct 2009EUROMECH Colloquium 512, Torino
Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 11/23
Risø, ETH, Tel Aviv Uni
Accuracy?
Oct 2009EUROMECH Colloquium 512, Torino
Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 12/23
Risø, ETH, Tel Aviv Uni
Accuracy?
Oct 2009EUROMECH Colloquium 512, Torino
Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 13/23
Risø, ETH, Tel Aviv Uni
Accuracy?
Oct 2009EUROMECH Colloquium 512, Torino
Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 14/23
Risø, ETH, Tel Aviv Uni
Accuracy?Nature 2003:
Oct 2009EUROMECH Colloquium 512, Torino
Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 15/23
Risø, ETH, Tel Aviv Uni
Acceleration magnitude
Oct 2009EUROMECH Colloquium 512, Torino
Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 16/23
Risø, ETH, Tel Aviv Uni
Acceleration magnitude
three distinct regions
Oct 2009EUROMECH 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 velocityright tail of PDF scales with -5/2
Oct 2009EUROMECH Colloquium 512, Torino
Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 18/23
Risø, ETH, Tel Aviv Uni
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
Oct 2009EUROMECH Colloquium 512, Torino
Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 19/23
Risø, ETH, Tel Aviv Uni
Curvaturewhy seemingly enstrophy dominated?al ac cancelation in high strain is low Re effect
Oct 2009EUROMECH Colloquium 512, Torino
Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 20/23
Risø, ETH, Tel Aviv Uni
Geometrical structure
Oct 2009EUROMECH Colloquium 512, Torino
Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 21/23
Risø, ETH, Tel Aviv Uni
Geometrical structure
1
3ω
ac
Oct 2009EUROMECH Colloquium 512, Torino
Small Scale Turbulence and Related Gradient Statistics Acceleration structure, 22/23
Risø, ETH, Tel Aviv Uni
Velocity acceleration structure function
Oct 2009EUROMECH 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 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