The understanding of fluid turbulence has considerably progressed in recent years. The application of the methods of statistical mechanics to the description of the motion of fluid particles, i.e., to the Lagrangian dynamics, has led to a new quantitative theory of intermittency in turbulent transport. The first analytical description of anomalous scaling laws in turbulence has been obtained. The underlying physical mechanism reveals the role of statistical integrals of motion in nonequilibrium systems. For turbulent transport, the statistical conservation laws are hidden in the evolution of groups of fluid particles and arise from the competition between the expansion of a group and the change of its geometry. By breaking the scale-invariance symmetry, the statistically conserved quantities lead to the observed anomalous scaling of transported fields. Lagrangian methods also shed new light on some practical issues, such as mixing and turbulent magnetic dynamo.

We consider inertial particles suspended in an incompressible turbulent flow. Because of particles' inertia their flow is compressible, which leads to fluctuations of concentration significant for heavy particles. We show that the statistics of these fluctuations is independent of details of the velocity statistics, which allows us to predict that the particles cluster on the viscous scale of turbulence and describe the probability distribution of concentration fluctuations. We discuss the possible role of the clustering in the physics of atmospheric aerosols, in particular, in cloud formation.

Strongly interacting electrons can move in a neatly coordinated way, reminiscent of the movement of viscous fluids. Here, we show that in viscous flows, interactions facilitate transport, allowing conductance to exceed the fundamental Landauer’s ballistic limit <mml:math><mml:msub><mml:mi>G</mml:mi><mml:mtext>ball</mml:mtext></mml:msub></mml:math>Gball . The effect is particularly striking for the flow through a viscous point contact, a constriction exhibiting the quantum mechanical ballistic transport at <mml:math><mml:mrow><mml:mpadded width="+1.7pt"><mml:mi>T</mml:mi></mml:mpadded><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>T=0 but governed by electron hydrodynamics at elevated temperatures. We develop a theory of the ballistic-to-viscous crossover using an approach based on quasi-hydrodynamic variables. Conductance is found to obey an additive relation <mml:math><mml:mrow><mml:mpadded width="+1.7pt"><mml:mi>G</mml:mi></mml:mpadded><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mtext>ball</mml:mtext></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mtext>vis</mml:mtext></mml:msub></mml:mrow></mml:mrow></mml:math>G=Gball+Gvis , where the viscous contribution <mml:math><mml:msub><mml:mi>G</mml:mi><mml:mtext>vis</mml:mtext></mml:msub></mml:math>Gvis dominates over <mml:math><mml:msub><mml:mi>G</mml:mi><mml:mtext>ball</mml:mtext></mml:msub></mml:math>Gball in the hydrodynamic limit. The superballistic, low-dissipation transport is a generic feature of viscous electronics.