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Three-dimensional turbulence simulations are used to show that the turbulent root mean square velocity is an upper bound of the speed of turbulent diffusion. There is a close analogy to magnetic diffusion where the maximum diffusion speed is the speed of light. Mathematically, this is caused by the inclusion of the Faraday displacement current which ensures that causality is obeyed. In turbulent diffusion, a term similar to the displacement current emerges quite naturally when the minimal tau approximation is used. Simulations confirm the presence of such a term and give a quantitative measure of its relative importance.

A short review of numerical simulation approaches for transitional and turbulent shear flows is presented. Some results using large-eddy simulation (LES) are for canonical turbulent and transitional flows obtained with different subgrid-scale (SGS) models such as a variant of the approximate deconvolution (ADM) and high-pass-filtered (HPF) eddy-viscosity model. Special focus is the LES of transition in incompressible flow.

Direct numerical simulations (DNS) of turbulent supersonic channel flow of air at Reynolds numbers ranging from = 180 to 560 and Mach numbers ranging from = 0.3 to 3.0 have been performed. The DNS data are used to explain the reduction of the pressure-correlation terms due to compressibility, using a Green’s function approach.

In this paper we consider a class of generalised diffusion equations which are of great interest in mathematical physics. For some of these equations that model fast diffusion new nonlocal potential symmetries are derived. These symmetries allow us to increase the number of solutions. These solutions are not arising from classical potential symmetries.

Lie group analysis is used to derive (exponential laws) for ZPG turbulent boundary layer flow. A new scaling group was found in the two-point correlation equations. DNS of such a flow was performed at = 2240 using a spectral method with up to 160 million grid points. The results of the numerical simulations are compared with the new scaling laws and good agreement is achieved.

By using small deviations from the stationary solution of the Navier-Stokes equation, the problem of linear instability of a plane submerged subsonic jet is considered. In the approximation of weak divergence of the jet, this problem reduces to a linear not self-adjoint boundary value problem with a given behavior of the variables at large values of the transversal coordinate. The solution of this boundary value problem allow us to calculate the gain factor and the phase velocity of hydrodynamical waves as functions of frequency and of distance from the nozzle. We have found that the dependence of the gain factor on the frequency has a resonant character. As the distance from the nozzle increases, the dependence of the gain factor on the frequency becomes more narrow and the maximum of that shifts into the small frequency region. Hence, the hydrodynamical waves become more and more coherent. The obtained results are in good agreement with experimental data.

One of the common views is that the behavior of passive objects in turbulent flows is in many respects similar to that of genuine turbulence. However, there exist a number of essential qualitative differences which require caution in promoting analogies between the two and which may be misleading. Some of these differences were summarized in [1]. It is the purpose of this note to provide a critical update of these essential differences with the emphasis on the aspects not given in [1] including the new results appeared after 2001.

By means of the Howard-Busse method of the optimum theory of turbulence we obtain numerical upper bound on the Nusselt number in a horizontal heated from below layer of fluid of finite Prandtl number. We show that for low and intermediate Rayleigh numbers the numerical bound is below the analytical bound obtained by Howard. For large Rayleigh numbers the numerical bound approaches the analytical asymptotic bound from below.

Based on Patent application DE 198 22 125.8-52, we present a technical description of a new temporal and spatial high resolving anemometer for gas and liquid flows. The measurement principle is based on the technique of an atomic force microscope where microstructured cantilevers are used to detect extreme small forces. We show the sensor as a small compact unit and present first measurements and characterizations.

The understanding of the complex statistics of fully developed turbulence in detail is still an open problem. One of the central points is to understand intermittency, i.e. to find exceptionally strong fluctuations on small scales. In the last years, the intermittency in different directions has attracted considerable interest. It has been controversial whether there are significant differences in intermittency between the different directions. More specifically one looks at the statistics of increments [( + ) − ()] , i.e. at the projection of the differences between two velocities separated by the vector in a certain direction . Here we denotes longitudinal increments with , for which and are parallel and transverse increments with for which is perpendicular to .

In a first step, one commonly investigates the statistics with the moments of the increments, the so-called structure functions, and assumes that, according to Kolmogorov, the structure functions obey a scaling law <> ∝ at least for sufficient high Reynolds number. The intermittency problem is then expressed by the deviation of the exponent ξ from the value /3, the well-known Kolmogorov (1941) scaling.