5,083 research outputs found
Scaling Laws and Intermittency in Highly Compressible Turbulence
We use large-scale three-dimensional simulations of supersonic Euler
turbulence to study the physics of a highly compressible cascade. Our numerical
experiments describe non-magnetized driven turbulent flows with an isothermal
equation of state and an rms Mach number of 6. We find that the inertial range
velocity scaling deviates strongly from the incompressible Kolmogorov laws. We
propose an extension of Kolmogorov's K41 phenomenology that takes into account
compressibility by mixing the velocity and density statistics and preserves the
K41 scaling of the density-weighted velocity v=rho^{1/3}u. We show that
low-order statistics of 'v' are invariant with respect to changes in the Mach
number. For instance, at Mach 6 the slope of the power spectrum of 'v' is -1.69
and the third-order structure function of 'v' scales linearly with separation.
We directly measure the mass dimension of the "fractal" density distribution in
the inertial subrange, D_m=2.4, which is similar to the observed fractal
dimension of molecular clouds and agrees well with the cascade phenomenology.Comment: 7 pages, 3 figures; in press, AIP Conference Proceedings: "Turbulence
and Nonlinear Processes in Astrophysical Plasmas", Waikiki Beach, Hawaii,
March 21, 200
Colloidal diffusion and hydrodynamic screening near boundaries
The hydrodynamic interactions between colloidal particles in small ensembles are measured at varying distances from a no-slip surface over a range of inter-particle separations. The diffusion tensor for motion parallel to the wall of each ensemble is calculated by analyzing thousands of particle trajectories generated by blinking holographic optical tweezers and by dynamic simulation. The Stokesian
Dynamics simulations predict similar particle dynamics. By separating the dynamics into three classes of modes: self, relative and collective diffusion, we observe qualitatively different behavior depending on the relative magnitudes of the distance of the ensemble from the wall and the inter-particle separation. A simple picture of the pair-hydrodynamic interactions is developed, while many-body-hydrodynamic interactions give rise to more complicated behavior. The results demonstrate that the
effect of many-body hydrodynamic interactions in the presence of a wall is much richer than the single
particle behavior and that the multiple-particle behavior cannot be simply predicted by a superposition of pair interactions
Shear thickening in colloidal dispersions
The popular interest in cornstarch and water mixtures known as “oobleck” after the complex fluid in one of Dr. Seuss's classic children's books arises from their transition from fluid-like to solid-like behavior when stressed. The viscous liquid that emerges from a roughly 2-to-1 (by volume) combination of starch to water can be poured into one's hand. When squeezed, the liquid morphs into a doughy paste that can be formed into shapes, only to “melt” into a puddle when the applied stress is relieved. Internet videos show people running across a large pool of the stuff, only to sink once they stop in place, and “monsters” that grow out of the mixture when it's acoustically vibrated (for an example, see the online version of this article)
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