Decorrelating a compressible turbulent flow: an experiment.

Floating particles that are initially distributed uniformly on the surface of a turbulent fluid, subsequently coagulate, until finally a steady state is reached. This being so, they manifestly form a compressible system. In this experiment, the information dimension D1, and the Lyapunov exponents of the coagulated floaters, is measured. The trajectories and the velocity fields of the particles are captured in a sequence of rapidly acquired images. Then the velocity sequence is randomly shuffled in time to generate new trajectories. This analysis mimics the Kraichnan ensemble and yields properties of a velocity correlation function that is delta correlated in time (but not in space). The measurements are compared with theoretical expectations and with simulations of Boffetta , that closely mimic the laboratory experiment reported here.

Power-law distributions of particle concentration in free-surface flows.

Particles floating on the surface of a turbulent incompressible fluid accumulate along string-like structures, while leaving large regions of the flow domain empty. This is reflected experimentally by a very peaked probability distribution function of c(r), the coarse-grained particle concentration at scale r, around c(r)=0, with a power-law decay over two decades of c(r), Pi(c(r)) proportional, variant c(r)(-beta(r)). The positive exponent beta(r) decreases with scale in the inertial range and stays approximately constant in the dissipative range, thus, indicating a qualitative difference between the dissipative and the inertial ranges of scales, also visible in the first moment of c(r).

Persistent global power fluctuations near a dynamic transition in electroconvection.

This is a study of the global fluctuations in power injection and light transmission through a liquid crystal just above the onset of electroconvection. The source of the fluctuations is identified as the creation and annihilation of defects. They are spatially uncorrelated and yet temporally correlated. The temporal correlation is seen to persist for extremely long times. There seems to be an especially close relation between defect creation or annihilation in electroconvection and thermal plumes in Rayleigh-Bénard convection.