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Rupture of an Amphiphile on airwater interface.

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The turbulent cascade in the right and in the wrong direction. Mahesh M. Bandi Pitt ... Atmospheric turbulence measurements using hot wire probe 35 m above ground. ... – PowerPoint PPT presentation

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Title: Rupture of an Amphiphile on airwater interface.


1
PV2/R
R
V
2
Fma (N-S Eq.)
acceleration
force/Kg
3
The turbulent cascade in the right and in the
wrong direction
Walter Goldburg (goldburg_at_pitt.edu)
  • Mahesh M. Bandi Pitt
  • John R. Cressman Jr GMU
  • Alain Pumir, CNRS Nice.

4
  • Often one measures the time average of
    fluctuations in velocity, energy dissipation,
    etc. at a point in the flow
  • Here we measure the spatial average of a property
    of the flow, the average being over the the scale
    of the largest eddies, lo
  • The trick new technology

5
Homogeneous isotropic turbulence
r ?
r l0
r
e
e
e
e
No energy dissipation in this inertial range
6
Integral scale l0 and dissipative scale ?
Ref U. Frisch, Turbulence, (Cambridge 1995)
7
Experimental Parameters.
8
the set-up
Pump
laser
1 m
Work station
High speed video camera
9
r
v(xr)
v(x)
10
  • Because the energy flux is just about the only
    variable for which there is an exact calculation
    of its average value.
  • In 1941 A. N. Kolmogorov derived the4/5 law.

Assumptions isotropy homogeniety (l0 infinite)
11
S3,being a random variable, fluctuates in time.
. For every r
We measure its PDF - averaged over all eddy sizes
r in the energy cascade range. Thus the
measurements represent a global average (over a
fraction of the total volume of the turbulent
fluid) made at many instants of time.
12
Visual Capture. Velocity Field
13
  • Tabelings Measurements of the third-moment.
  • Zocchi et. al. PRE 50, 3693, (1994) Tabeling
    et. al. PRE 53, 1613 (1996).
  • Liquid Helium driven by counter-rotating disks.
    Re? 174 5040.

14
  • Sreenivasans Measurements of the third-moment.
  • Sreenivasan et. al. http//arxiv.org/abs/chao-dyn
    /9906041 (1999)
  • Atmospheric turbulence measurements using hot
    wire probe 35 m above ground.

15
Experimental Procedure.
Movie capture with CCD Camera. 5 second movie
broken into 2040 TIFF images.
Velocity field reconstruction. Input Pair of
TIFF Images. Output Velocity field.
Calculation of Moments. S3(r)
Spatial averaging PDF -e(t) S3(r)/(4/5)r
16
Verifying the four-fifths law.
17
How wild are the third-moment fluctuations?
18
PDF of Spatially Averaged Energy Transfer Rate.
19
PDF of Spatially Averaged Energy Transfer Rate.
20
How often does the Energy Cascade reverse
direction?
21
  • Simulation (No theory).
  • Enter Smooth Particle Hydrodynamics.
  • - ?t, a dimensionless constant, not to be
    confused with kinematic viscosity.
  • - vij, velocity difference between two points
    separated by distance rij.
  • - h, the smoothing distance over which all
    fluctuations are averaged out.
  • Pumir Shraiman. Lagrangian particle approach
    to large eddy simulations of hydrodynamic
    turbulence, J. Stat. Phys. 113, 693 (2003).

22
When computed over entire volume of the
Simulation Box.
23
When computed over a sub-domain (1/4th size of
Simulation Box).
24
  • Summary.
  • A study the PDF of spatially-averaged
    fluctuations in the flux of energy through a
    turbulent 3D fluid
  • The energy-cascade frequently reverses its
    direction (25 of the time)
  • the energy in small scales is momentarily being
    returned to large spatial scales.
  • Numerical Simulations also demonstrate momentary
    energy-cascade reversals.
  • A theory exists for the average flux large to
    small scales but not for flux PDF.

25
Talk ends with previous slide
26
  • Outline.
  • Motivation
  • Past Measurements
  • Whats different about our Experiment?
  • Experimental Procedure.
  • Description of the Experimental Setup.
  • The spatially and temporally averaged
    third-moment.
  • Time trace and PDF of energy transfer rate.

27
The Energy Cascade Process. Direction of energy
cascade.
Kolmogorovs four-fifths law
28
  • the average velocity at a point
  • the nth moment of velocity differences between
    two closely spaced points
  • The mean rate at which energy is dissipated in
  • J / Kg s

Kinematic viscosity
29
  • Dan Lathrops measurements in 3D.
  • Zeff, B. et. al. Nature 421, 146 (2003).

30
Visual Capture. CCD Movie
31
  • Re-expressing the Third-moment.
  • The spatially averaged steady-state Energy
    Transfer Rate.
  • It has also been re-derived by Andersen et. al.
    to hold for Lagrangian measurements.
  • Note e is positive, making S3(r) negative
  • Mann, J., Ott, S. Andersen, J. S. Experimental
    study of relative, turbulent diffusion.

32
  • In the study of turbulence, one usually measures
    the average value of various quantities, A.
  • These quantities are random variables and hence
    have a PDF associated with them
  • Here we focus on the flux of energy through a
    turbulent system. Why?

33
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34
S.T. Bramwell et al. Nature, 396, 552 (1998)
P.Tabeling et al., Phys. Rev. E .53, 1613 (1996)
35
  • The third-moment in all past measurements was
    obtained from time-averages.
  • Provides mean energy transfer rate of fluid, but
    says nothing about fluctuations.
  • We are interested in fluctuations about the mean
    Energy Flux.
  • Can measure third-moment at various spatial
    scales at every instant of time.
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