1,626 research outputs found
Evolution of isolated turbulent trailing vortices
In this work, the temporal evolution of a low swirl-number turbulent Batchelor vortex is studied using pseudospectral direct numerical simulations. The solution of the governing equations in the vorticity-velocity form allows for accurate application of boundary conditions. The physics of the evolution is investigated with an emphasis on the mechanisms that influence the transport of axial and angular momentum. Excitation of normal mode instabilities gives rise to coherent large scale helical structures inside the vortical core. The radial growth of these helical structures and the action of axial shear and differential rotation results in the creation of a polarized vortex layer. This vortex layer evolves into a series of hairpin-shaped structures that subsequently breakdown into elongated fine scale vortices. Ultimately, the radially outward propagation of these structures results in the relaxation of the flow towards a stable high-swirl configuration. Two conserved quantities, based on the deviation from the laminar solution, are derived and these prove to be useful in characterizing the polarized vortex layer and enhancing the understanding of the transport process. The generation and evolution of the Reynolds stresses is also addressed
Qualitative application of a result in control theory to problems of economic growth
Qualitative application of result in control theory to problem of economic growt
Strain-Rate Frequency Superposition in Large-Amplitude Oscillatory Shear
In a recent work, Wyss, {\it et.al.} [Phys. Rev. Lett., {\bf 98}, 238303
(2007)] have noted a property of `soft solids' under oscillatory shear, the
so-called strain-rate frequency superposition (SRFS). We extend this study to
the case of soft solids under large-amplitude oscillatory shear (LAOS). We show
results from LAOS studies in a monodisperse hydrogel suspension, an aqueous
gel, and a biopolymer suspension, and show that constant strain-rate frequency
sweep measurements with soft solids can be superimposed onto master curves for
higher harmonic moduli, with the {\it same} shift factors as for the linear
viscoelastic moduli. We show that the behavior of higher harmonic moduli at low
frequencies in constant strain-rate frequency sweep measurements is similar to
that at large strain amplitudes in strain-amplitude sweep tests. We show
surface plots of the harmonic moduli and the energy dissipation rate per unit
volume in LAOS for soft solids, and show experimentally that the energy
dissipated per unit volume depends on the first harmonic loss modulus alone, in
both the linear and the nonlinear viscoelastic regime.Comment: 10 pages, 25 figures, accepted for publication in Physical Review E.
Incorporates referee comment
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
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