Vorticity fluctuations

Tennekes and Lumley [167] find it more appropriate to list the characteristics of turbulent flow such as Irregularity (or randomness), diffusivity, large Reynolds numbers, three dimensional vorticity fluctuations and dissipation. Turbulence is not a feature of fluids, but of fluid flows thus a continuum... 

Fig. 4 Distribution of streamwise vorticity fluctuations normalized with the friction velocity and kinematic viscosity in the vicinity of the wall.

Fig. 6 Distribution of skewness and flatness factors for the streamwise vorticity fluctuations. A Kreplin and Eckelmann (21). From (22)...

Figure 1.9 Comparison between the semi-implicit/explicit and the fully implicit scheme for the rms vorticity fluctuations. (Adapted from Ref [55].)...

By decomposing the vorticity into a mean Zj and a fluctuation u, the mean baroclinic generation terms are... 

Figure 11.4 Radial distributions of the RMS of the fluctuating vorticity components at different times for the unheated (left column) and heated (right column) jet. The times are t = 25 (dotted curve), f = 30 (dashed curve), and f = 35 (solid curve)... 

This type of process is missing from U(l) quantum field theory [6] the B(3> field produces quantum vortices [17] that interact with electrons and other charged particles. The vortices are quantized states and exist as fluctuations in the QED vacuum, fluctuations that are associated, not with an E(3) field, but with the = E(1> fields ... 

Remark. Instability and bistability are defined as properties of the macroscopic equation. The effect of the fluctuations is merely to make the system decide to go to one or the other macroscopically stable point. Similarly the Taylor instability and the Benard cells are consequences of the macroscopic hydrodynamic equations. ) Fluctuations merely make the choice between different, equally possible macrostates, and, in these examples, determine the location of the vortices or of the cells in space. (In practice they are often overruled by extraneous influences, such as the presence of a boundary.) Statements that fluctuations shift or destroy the bistability are obscure, because on the mesoscopic level there is no sharp separation between stable and unstable systems. Some authors call a mesostate (i.e., a probability distribution P) bistable when P has two maxima, however flat. This does not correspond to any observable fact, however, unless the maxima are well-separated peaks, which can each be related to separate macrostates, as in (1.1). 

In fig.4 (lower panel) it is schematically presented the structure of the SC vortex in the SDW/CDW + SC state. Since arising of the CDW results in the lattice modulation so that wave of dislocation walls is formed (fig.4 (middle panel)). As known, such dislocation walls are effective centers for pinning of SC vortices. Note that in such a structure every fifth wall is equivalent to first one ( cn+4 - c ). In this a model a vortex core has AF SDW structure which is also outside a core too. Because of equivalence of c and c +4 dislocation walls vortex core becames to be two part in form fluctuating in space (cf. with [14]). 

These fluctuations maybe caused by rapid variations in pressure or velocity producing random vortices and flow instabilities within the fluid. A complete mathematical analysis of turbulent flow remains elusive due to the erratic nature of the flow. Often used to promote mixing or enhance transport to surfaces, turbulent flow has been studied using electrochemical techniques [i]. 

Continuum Depiction Local oscillation of the melt-wall boundary condition in the exit region causes peturbations on the exit stress and die swell Oscillation of the overall stress due to unstable boundary condition produces cycles of melt compression and decompression in the barrel and fluctuations in the extrude swell The extrudate distortion arises from formation of secondary flow (vortices) in the barrel due to the strong converging flow near the die entry... 

---