1. Turbulence Academic Engineering Difficult!!!! Boundaries Re is never inf. Anisotropic Non-Stationary Emphasize on large scales Developed Re>>1 (? about small scales) vs Phenomenology * ’30-’50* (von Karman,Kolmogorov,Obukhov,Corrsin, Heisenberg,Onsager) Wave Turb, Inverse-Direct, ** (Models: Kraichnan, Batchelor, Kazantsev, Zeldovich) ’60-’80 Statistical Hydrodynamics (Scalar Turb *, Burgulence, ’90-* Intermittency, Anomalous scaling, …) Non-Equilibrium Statistical Physics Rayleigh-Taylor ** Acceler. of chem.react. by turb. Chaotic flows Kinematic dynamo Shock/Collapse turbulence Elastic Turbulence DNS, LES Table-top (physics) experiment

2. Navier-Stokes Turbulence Phenomenology Navier-Stokes Turbulence Phenomenology (steady 3d) cascade integral (pumping) scale viscous (Kolmogorov) scale kinetic energy flux scale independent !!! scale independent !!! time independent !!! time independent !!! typical velocity fluctuation on scale “r” Kolmogorov ’41 Obukhov ‘41 * 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. the inverse cascade for two-dimensional turbulence inverse Kraichnan’s 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. Zakharov’s 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 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 + Field formulation (Eulerian) Particles Particles (“QM”) (Lagrangian)

5. Phenomenology of Rayleigh-Taylor Turbulence Boussinesq L(t) ~ turbulent (mixing) zone width also energy-containing scale also energy-containing scale Sharp-Wheeler ’61 Input: Idea: Cascade + Adiabaticity: - decreases with r Results: 3d 2d “passive” “buoyant” viscous and diffusive scales decrease with timeincrease with time M. Chertkov, PRL 2003 * (extends to the generic misscible case) consistent with Clark,Ristorcelli ‘03 Setting: