Eddies initiation

For flow past a cyhnder, the vortex street forms at Reynolds numbers above about 40. The vortices initially form in the wake, the point of formation moving closer to the cylinder as Re is increased. At a Reynolds number of 60 to 100, the vortices are formed from eddies attached to the cylinder surface. The vortices move at a velocity slightly less than V. The frequency of vortex shedding/is given in terms of the Strouhal number, which is approximately constant over a wide range of Reynolds numbers. 

If a turbulent fluid passes into a pipe so that the Reynolds number there is less than 2000, the flow pattern will change and the fluid will become streamline at some distance from the point of entry. On the other hand, if tire fluid is initially streamline (Re < 2000), the diameter of the pipe can be gradually increased so that the Reynolds number exceeds 2000 and yet streamline flow will persist in the absence of any disturbance. Unstable streamline flow has been obtained in this manner at Reynolds numbers as high as 40,000. The initiation of turbulence requires a small force at right angles to the flow to promote the formation of eddies. 

The work of Higbie laid the basis of the penetration theory in which it is assumed that the eddies in the fluid bring an element of fluid to the interface where it is exposed to the second phase for a definite interval of time, after which the surface element is mixed with the bulk again. Thus, fluid whose initial composition corresponds with that of the bulk fluid remote from the interface is suddenly exposed to the second phase. It is assumed that equilibrium is immediately attained by the surface layers, that a process... 

Bubble and drop breakup is mainly due to shearing in turbulent eddies or in velocity gradients close to the walls. Figure 15.11 shows the breakup of a bubble, and Figure 15.12 shows the breakup of a drop in turbulent flow. The mechanism for breakup in these small surface-tension-dominated fluid particles is initially very similar. They are deformed until the aspect ratio is about 3. The turbulent fluctuations in the flow affect the particles, and at some point one end becomes... 

Smirnova, J. B., Selley, J. N., Sanchez-Cabo, F., Carroll, K., Eddy, A. A., McCarthy, J. E., Hubbard, S. J., Pavitt, G. D., Grant, C. M., and Ashe, M. P. (2005). Global gene expression profiling reveals widespread yet distinctive translational responses to different eukaryotic translation initiation factor 2B-targeting stress pathways. Mol. Cell Biol. 25, 9340-9349. 

The scalar integral scale characterizes the largest structures in the scalar field, and is primarily determined by two processes (1) initial conditions - the scalar field can be initialized with a characteristic that is completely independent of the turbulence field, and (2) turbulent mixing - the energy-containing range of a turbulent flow will create scalar eddies with a characteristic length scale I.,p that is approximately equal to Lu. 

During the time intervals between random eddy events, (4.37) is solved numerically using the scalar fields that result from the random rearrangement process as initial conditions. A standard one-dimensional parabolic equation solver with periodic boundary conditions (BCs) is employed for this step. The computational domain is illustrated in Fig. 4.3. For a homogeneous scalar field, the evolution of t) will depend on the characteristic length... 

Figure 1-7 Evolution of concentration profiles for (a) one-dimensional point-source diffusion and (b) 3-D point-source diffusion. This calculation is made for M= 100 kg/m, and Oeddy lO " ui /s (eddy diffusivity). in the 3-D case, C was much higher at the center at smaller times because initial mass distribution was at a point instead of a plane but at greater times, the concentration dissipates much more rapidly.

Carboxylic acids The smallest carboxylic acid, formic acid, can be measured using infrared spectroscopy (Table 11.2), since it has characteristic absorption bands. As discussed earlier and seen in Fig. 11.33b, mass spectrometry with chemical ionization using SiF5 also revealed HCOOH in an indoor environment (Huey et al., 1998). However, since the sensitivity in these initial studies was about two orders of magnitude less than that for HN03, the detection limit may be about the same as that for FTIR and TDLS. Formic and acetic acids have been monitored continuously from aircraft (Chapman et al., 1995) and their surface flux determined by eddy correlation (Shaw et al., 1998) using atmospheric pressure ionization mass spectrometry. Detection limits are about 30 ppt. 

Let us make this point clearer by the following hypothetical experiment. At some initial time t0 a droplet of dye is put on the surface of a turbulent fluid (Fig. 22.9). At some later time t] the large-scale fluid motion has moved the dye patch to a new location which can be characterized by the position of the center of mass of the patch. In addition, the patch has grown in size because of the small (turbulent) eddies, more precisely, those eddies with sizes similar to or smaller than the patch size. 

A flow of argon in which ionisation has been initiated by a tesla discharge passes through an open quartz tube. A water-cooled copper tube is coiled around the quartz tube (Fig. 15.1). The copper tubing is connected to a radiofrequency generator (typically at 27 MHz) with a power of 1 to 2 kilowatts. The variable magnetic field that is created confines the ions and electrons to an annular path (with the appearance of an eddy current). As this environment becomes more and... 

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