The spectral analysis of multichannel magnetoencephalographic data is presented. This analysis revealed a local similarity regime in brain activity ͑in more than two decades of frequencies͒ and provided new parameters for noninvasive experimental studies of the brain.

We present some preliminary results from using large-eddy simulation to compute the late wake of a sphere towed at constant speed through a non-stratified and a uniformly stratified fluid. The wake is computed in each case for two values of the Reynolds number: Re = 104, which is comparable to that used in laboratory experiments, and Re = 105. An important aspect of the simulation is the use of an iterative procedure to relax the initial turbulence field so that the normal and shear turbulent stresses are properly correlated and the turbulent production and dissipation are in equilibrium. For the lower Reynolds number our results compare well with existing laboratory experimental results. For the higher Reynolds number we find that even though the turbulence is more developed and the wake contains finer structure, most of the similarity properties of the wake are unchanged compared with those observed at the lower Reynolds number.

It is shown that the hypothesis of independent increments for velocity, which is widely used by many authors [e.g., A. M. Obukhov, Adv. Geophys. 6, 113 (1959)] in the Lagrangian description of turbulence, is inconsistent with the Navier–Stokes equations in a fundamental way. A more general Lagrangian description of turbulent velocity such as the Markov process with dependent increments, which recognizes the condition of incompressibility and the important phenomenon of intermittency, is proposed. A model of intermittent relative motion of fluid particles in turbulent flow is presented. The high-order Lagrangian moments and the probability distribution are obtained. The distribution for the intermittent vorticity is also proposed.

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We consider Lagrangian stochastic modelling of the relative motion of two fluid particles in the inertial range of a turbulent flow. Eulerian analysis of such modelling corresponds to an equation for the Eulerian probability distribution of velocity-vector increments which introduces a hierarchy of constraints for making the model consistent with results from the theory of locally isotropic turbulence. A nonlinear Markov process is presented, which is able to satisfy exactly, in the statistical sense, incompressibility, the exact results on the third-order structure function, and the experimental second-order statistics. The corresponding equation for the Eulerian probability density of velocity-vector increments is solved numerically. Numerical results show non-Gaussian statistics of the one-dimensional Lagrangian probability distributions, and a complex shape of the three-dimensional Eulerian probability density function. The latter is then compared with existing experimental data.

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A statistical description of droplets in turbulent spray, connected with the description of turbulent dissipation, is presented. The ideas of similarity, the cascade processes, and the infinitely divisible distributions are used in this description. Formulas for characteristic droplet sizes and corresponding probability distributions are obtained along with a simple formula for turbulent dissipation in flow near a ship.

The relations between Lagrangian and Eulerian probabilities are obtained for the case of variable density of fluid. The general stochastic model for trajectories in nonhomogeneous turbulence is considered, and probability for Lagrangian forcing is expressed in terms of Eulerian distribution. The criterion of the influence of boundaries on the asymptotic behavior of trajectories is presented.