Flow-parametric regulation of shear-driven phase separation in two and three dimensions.

The Cahn-Hilliard equation with an externally prescribed chaotic shear flow is studied in two and three dimensions. The main goal is to compare and contrast the phase separation in two and three dimensions, using high-resolution numerical simulation as the basis for the study. The model flow is parametrized by its amplitudes (thereby admitting the possibility of anisotropy), length scales, and multiple time scales, and the outcome of the phase separation is investigated as a function of these parameters as well as the dimensionality.

Statistical mechanics of Beltrami flows in axisymmetric geometry: theory reexamined.

A simplified thermodynamic approach of the incompressible axisymmetric Euler equations is considered based on the conservation of helicity, angular momentum, and microscopic energy. Statistical equilibrium states are obtained by maximizing the Boltzmann entropy under these sole constraints. We assume that these constraints are selected by the properties of forcing and dissipation.

Scale dependence of the coarse-grained velocity derivative tensor structure in turbulence.

Velocity fluctuations in hydrodynamic turbulence have a nontrivial structure, characterized by correlations of the velocity gradient tensor. In this paper, we consider a phenomenological model, incorporating the main features of hydrodynamic fluid turbulence, aimed at predicting the structure of the velocity gradient tensor coarse grained at a spatial scale r. This model [M.

Transition to spatiotemporal chaos in a two-dimensional hydrodynamic system.

We study the transition to spatiotemporal chaos in a two-dimensional hydrodynamic experiment where liquid columns take place in the gravity induced instability of a liquid film. The film is formed below a plane grid which is used as a porous media and is continuously supplied with a controlled flow rate. This system can be either ordered (on a hexagonal structure) or disordered depending on the flow rate.