Turbulence: Out of troubled waters?

Turbulence is often referred to as the last unsolved problem in classical physics. This leads to the discouraging impression that turbulence is an almost impossible challenge, where fundamental progress is hardly possible, and where problems of applied importance can be only treated using ad-hoc approximations.

Over the last few years, however, there has been very pronounced progress in understanding the fundamentals of turbulence. Many deep theoretical results have been obtained in the problem of mixing of a passive scalar by a turbulent flow, opening new perspectives on the turbulence problem itself. This progress is intrinsically related to the very stimulating developments in Lagrangian measurements and theory. These recent achievements have brought to light further fundamental problems, making the subject more diverse, and in scientific terms, even more interesting. The old problem as to whether small scales become isotropic at high Reynolds number is currently the subject of renewed debate and the existence of the relationship between anisotropy and intermittency is being examined in the light of the new evidence. The issue of the dependency of the small scales on the large scale boundary conditions is beginning to be systematically explored. And how modelling, such as Large Eddy Simulations, can deal with solid boundaries and with small scale anomalies is still an open question, but one in which there is great activity.

The purpose of this issue in New Journal of Physics is to address these and other basic questions in turbulence theory, experiment, computation and modelling, highlighting where progress has been achieved, and where it can be reasonably expected within the next few years. Listed below are the first contributions. Further articles from other leading groups in the field will appear in the near future.

Elastic turbulence in curvilinear flows of polymer solutions
Alexander Groisman and Victor Steinberg

Small-scale anisotropy in stably stratified turbulence
Yukio Kaneda and Kyo Yoshida

Ten questions concerning the large-eddy simulation of turbulent flows
Stephen B Pope

Anomalous scaling and universality in hydrodynamic systems with power-law forcing
L Biferale, M Cencini, A S Lanotte, M Sbragaglia and F Toschi

On conditional scalar increment and joint velocity–scalar increment statistics
Hengbin Zhang, Danhong Wang and Chenning Tong

Statistics of a passive scalar in homogeneous turbulence
Takeshi Watanabe and Toshiyuki Gotoh

Markovian properties of passive scalar increments in grid-generated turbulence
M Tutkun and L Mydlarski

Entropy production and extraction in dynamical systems and turbulence
Gregory Falkovich and Alexander Fouxon

Eulerian and Lagrangian studies in surface flow turbulence
John R Cressman, Jahanshah Davoudi, Walter I Goldburg and Jörg Schumacher

Conditional scalar mixing statistics in homogeneous isotropic turbulence
B L Sawford

A low-dimensional model for turbulent shear flows
Jeff Moehlis, Holger Faisst and Bruno Eckhardt

Particle pair diffusion and persistent streamline topology in two-dimensional turbulence
Susumu Goto and J C Vassilicos

Active and passive fields face to face
Antonio Celani, Massimo Cencini, Andrea Mazzino and Massimo Vergassola

Advances in wave turbulence: rapidly rotating flows
C Cambon, R Rubinstein and F S Godeferd

Experimental and numerical study of the Lagrangian dynamics of high Reynolds turbulence
Nicolas Mordant, Emmanuel Lévêque and Jean-François Pinton

Reynolds number scaling of particle clustering in turbulent aerosols
Lance R Collins and Arun Keswani

Unifying ideas on mixing and atomization
Emmanuel Villermaux

Progress in studying small-scale turbulence using 'exact' two-point equations
L Danaila, R A Antonia and P Burattini

Lagrangian statistics for fluid particles and bubbles in turbulence
Irene M Mazzitelli and Detlef Lohse

On the distribution of Lagrangian accelerations in turbulent flows
A M Reynolds, N Mordant, A M Crawford and E Bodenschatz

Zellman Warhaft, Cornell University, NY, USA
Alain Pumir, Institut Non Linéaire de Nice Sophia Antipolis, France