The Kolmogorov-Batchelor-Kraichnan (KBK) theory of two-dimensional turbulence is generalized for turbulence on the surface of a rotating sphere. The energy spectrum develops considerable anisotropy; a steep -5 slope emerges in the zonal direction, while in all others the classical KBK scaling prevails. This flow regime in robust steady state is reproduced in simulations with linear drag. The co...

Relative dispersion of a passive scalar plume was investigated in uniformly sheared, nearly homogeneous, turbulent flow with Reλ≈150 using planar laser-induced fluorescence. Mean concentration maps were determined both in the laboratory frame and in a frame attached to the instantaneous center of mass of the plume cross section. The distance-neighbor function had a shape that was compatible wit...

We report experiments on mixing of a passively advected fluorescent dye in a low Reynolds number flow in a microscopic channel. The channel is a chain of repeating segments with a custom designed profile that generates a steady three-dimensional flow with stretching and folding, and chaotic mixing. A few statistical characteristics of mixing in the flow are studied and are all found to agree wi...

A phenomenological model for the dissipation of scalar fluctuations due to the straining by the fluid motion is proposed in this Brief Communication. An explicit equation is obtained for the time evolution of the probability distribution function of a coarse-grained scalar concentration. The model relies on a self-convolution process. We first present this model in the Batchelor regime and then...

Bounds on high-order derivative moments of a passive scalar are obtained for large values of the Schmidt number, Sc. The procedure is based on the approach pioneered by Batchelor for the viscous–convective range. The upper bounds for derivative moments of order n are shown to grow as Sc for very large Schmidt numbers. The results are consistent with direct numerical simulations of a passive sca...

M. Chertkov,1 G. Falkovich,2 and I. Kolokolov3 1Physics Department, Princeton University, Princeton, New Jersey 08544 2Institute for Advanced Study, Princeton, New Jersey and Weizmann Institute, Rehovot, Israel 3Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia (Received 3 September 1997) The probability density function (PDF) of passive scalar dissipation P sed is found analytica...

Twelve patients (17 feet) with progressive neuromuscular planovalgus foot deformity underwent an extra-articular subtalar arthrodesis with the combined Batchelor-Grice procedure. All patients were ambulant and received conservative treatment with braces and special orthopaedic shoes before the operation. Postoperatively the feet were immobilized in short leg casts for 6 weeks. Evaluation was ba...

We present a scaling theory for unforced inviscid two-dimensional turbulence. Our model unifies existing spatial and temporal scaling theories. The theory is based on a self-similar distribution of vortices of different sizes A. Our model uniquely determines the spatial and temporal scaling of the associated vortex number density which allows the determination of the energy spectra and the vort...

We prove that a certain class of elliptic free boundary problems, which includes the Prandtl–Batchelor problem from fluid dynamics as special case, has two distinct nontrivial solutions for large values parameter. The first solution is global minimizer energy. energy functional nondifferentiable, so standard variational arguments cannot be used directly to obtain second solution. our limit moun...