Geophysical Applications (rain) etc. New ideas (e.g

1
Turbulence
Academic
Engineering
vs
Difficult!!!! Boundaries Re is never
inf. Anisotropic Non-Stationary Emphasize on
large scales
Developed Regtgt1 (? about small scales)
DNS, LES
Phenomenology 30-50 (von Karman,Kolmogorov,Obu
khov,Corrsin, Heisenberg,Onsager) Wave Turb,
Inverse-Direct, (Models Kraichnan,
Batchelor, Kazantsev, Zeldovich)
60-80 Statistical Hydrodynamics (Scalar Turb
, Burgulence, 90- Intermittency, Anomalous
scaling, )

Rayleigh-Taylor Acceler. of chem.react. by
turb. Chaotic flows Kinematic
dynamo Shock/Collapse turbulence Elastic
Turbulence
Table-top (physics) experiment
Non-Equilibrium Statistical Physics
2
Navier-Stokes Turbulence Phenomenology
(steady 3d)
kinetic energy flux scale independent !!! time
independent !!!
Kolmogorov 41 Obukhov 41
typical velocity fluctuation on scale r
Universality !!!

3
2003 Dirac Medal    On the occasion of the
birthday of P.A.M. Dirac the Dirac Medal
Selection Committee takes pleasure in announcing
that the 2003 Dirac Medal and Prize will be
awarded to Robert H. Kraichnan (Santa Fe, New
Mexico)  and  Vladimir E. Zakharov (Landau
Institute for Theoretical Physics)   The 2003
Dirac Medal and Prize is awarded to Robert H.
Kraichnan and Vladimir E. Zakharov for their
distinct contributions to the theory of
turbulence, particularly the exact results and
the prediction of inverse cascades, and for
identifying classes of turbulence problems for
which in-depth understanding has been
achieved.   Kraichnans most profound
contribution has been his pioneering work on
field-theoretic approaches to turbulence and
other non-equilibrium systems one of his
profound physical ideas is that of the inverse
cascade for two-dimensional turbulence.
Zakharovs achievements have consisted of putting
the theory of wave turbulence on a firm
mathematical ground by finding turbulence spectra
as exact solutions and solving the stability
problem, and in introducing the notion of inverse
and dual cascades in wave turbulence.         8
August 2003

4
Intermittency (anomalous scaling) of
density/temperature fluctuations
Small scale fluctuations of passive scalar shows
intermittency (and anisotropy) even in a
self-similar velocity field !!!! Kraichnan
model 1/d-expansion
Chertkov, Falkovich, Kolokolov,Lebedev 95
almost diffusive
limit Gawedzki, Kupianen 95
almost smooth limit
Shraiman, Siggia 95 exponent
saturation (large n) Chertkov 97
Balkovsky, Lebedev 98 Lagrangian numerics
Frisch,Mazzino,Vergassola 99


Field formulation (Eulerian)
Particles (QM) (Lagrangian)
Lagrangian Phen. for NS (towards LES) Kinematic
Dynamo Theory Chemical Reaction in Turb.
Geophysical Applications (rain) etc
New ideas (e.g. Lagrangian,instanton) New objects
to study New emphasize on strucures/statistics
relation


5
Phenomenology of Rayleigh-Taylor Turbulence
M. Chertkov, PRL 2003
Setting
L(t) turbulent (mixing) zone width
also energy-containing scale
Input
Boussinesq
Sharp-Wheeler 61
(extends to the generic misscible case)
Idea Cascade Adiabaticity
- decreases with r
Results
2d
3d
buoyant
passive
viscous and diffusive scales
consistent with Clark,Ristorcelli 03