Time evolution of a fractal distribution: Particle concentrations in free-surface turbulence

Steady-state turbulence is generated in a tank of water and the trajectories of particles forming a compressible system on the surface are tracked in time. The initial uniformly distributed floating particles coagulate and form a fractal structure, a rare manifestation of a strange attractor observable in real space. The surface pattern reaches a steady state in approximately 1 s. Measurements are made of the fractal dimensions D_q(t) (q=1 to 6) of the floating particles starting with the uniform distribution D_q(0)=2 for Taylor Microscale Reynolds number Re_λ?160. Focus is on the time evolution of the correlation dimension D₂(t) as the steady state is approached. This steady state is reached in several large eddy turnover times and does so at an exponential rate.     

Test of the Fluctuation Relation in Lagrangian Turbulence on a Free Surface

The statistics of velocity divergence are studied for an assembly of particles that float on a closed turbulent fluid. Under an appropriate definition of entropy, the two-dimensional Lagrangian velocity divergence of a particle trajectory represents the local entropy rate , a random variable in time. The statistics of this rate, measured in the Lagrangian frame, are collected over a wide range of values. This permits a severe test of the fluctuation relation (FR) over a range that exceeds prior experiments, out to a regime beyond which the FR no longer holds. Notably, the probability density functions (PDF) of the dimensionless divergence σ _τ are strongly non-Gaussian. This work was supported by the National Science Foundation under grant number DMR-0201805.     

Where surface physics and fluid dynamics meet: rupture of an amphiphile layer by fluid flow

We investigate the fluctuating pattern created by a jet of fluid impingent upon an amphiphile-covered surface. This microscopically thin layer is initially covered with 50 microm floating particles so that the layer can be visualized. A vertical jet of water located below the surface and directed upward drives a hole in this layer. The hole is particle-free and is surrounded by the particle-laden amphiphile region. The jet ruptures the amphiphile layer creating a particle-free region that is surrounded by the particle-covered surface. The aim of the experiment is to understand the (fluctuating) shape of the ramified interface between the particle-laden and particle-free regions.