Title: Rupture of an Amphiphile on airwater interface.
1PV2/R
R
V
2Fma (N-S Eq.)
acceleration
force/Kg
3The 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
5Homogeneous isotropic turbulence
r ?
r l0
r
e
e
e
e
No energy dissipation in this inertial range
6Integral scale l0 and dissipative scale ?
Ref U. Frisch, Turbulence, (Cambridge 1995)
7Experimental Parameters.
8the set-up
Pump
laser
1 m
Work station
High speed video camera
9r
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)
11S3,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.
12Visual 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.
15Experimental 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
16Verifying the four-fifths law.
17How wild are the third-moment fluctuations?
18PDF of Spatially Averaged Energy Transfer Rate.
19PDF of Spatially Averaged Energy Transfer Rate.
20How 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).
22When computed over entire volume of the
Simulation Box.
23When 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.
25Talk 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.
27The 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).
30Visual 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(No Transcript)
34S.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.