Wakes vorticity

Wickens, R. H. "A technique for simulating the motion and ground effect of aircraft wake vortices-with particular reference to the spraying of insecticides." LTR-LA-186, Natl. Aeronaut. Establ., Natl. Res. Counc. Can., Ottawa, 1975. 

When there are marked variations in the height of adjacent obstacles, the wake vorticity shed from upwind buildings can produce sharp down-flows and increased trailing vorticity in the flow direction, (see Lawson, 1980 [360]). These effects contribute to mixing between the canopy and external flow, Figure 2.6. When tall cuboid obstacles are closely packed (i.e. H/w > 1, b/d > 1/2), as the air flow passes around them the wakes tend to disappear (because of cancellation of vorticity) and the streamlines are determined simply by the displacement or blocking effects of the buildings (Davidson et al., 1995 [143] Moulinec et al., 2003 [436]). 

The total dipole strength induced by a rigid body in a straining flow is approximately the sum of (7.7) and (7.17). The relationship between drag and volume flux is now no longer valid for when the wake vorticity is partially or completely annihilated, and is now determined by the local strain rate through... 

The disappearance of the wake vorticity leads to an irrotational dipolar flow (see the analysis of (7.2.2)) of strength... 

Fig. 3. Flow past a circular cylinder for (a). Re < 5 where no separation is evident (b) 5 < Re < 40 and fixed vortices exist in a separation bubble or wake ...

As the Reynolds number rises above about 40, the wake begins to display periodic instabiUties, and the standing eddies themselves begin to oscillate laterally and to shed some rotating fluid every half cycle. These still laminar vortices are convected downstream as a vortex street. The frequency at which they are shed is normally expressed as a dimensionless Strouhal number which, for Reynolds numbers in excess of 300, is roughly constant ... 

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. 

For 40 < Re < 200 the vortices are laminar and the Strouhal number has a nearly constant value of 0.2 for flow past a cylinder. Between Re = 200 and 400 the Strouhal number is no longer constant and the wake becomes irregular. Above about Re = 400 the vortices become turbulent, the wake is once again stable, and the Strouhal number remains constant at about 0.2 up to a Reynolds number of about 10. ... 

Blade stall causes Karman vortices in the airfoil wake. Whenever the frequency of these vortices coincides with the natural frequency of the airfoil, flutter will occur. Stall flutter is a major cause of compressor blade failure. 

It has also been shown, using visual illustrative methods, that accumulation can occur in the wake of people or objects, provided that the contaminants are emitted in the vortex region. Special consideration must be taken with instabilities and vortices generated by the working person. Vortices can also occur in empty open unidirectional airflow benches. 

Essenriatiy, vortices caused by people are of two kinds. Relatively stable and stationary wakes are created by the body. Unstable and nonstationary vortices arise... 

As the fluid flows over the forward part of the sphere, the velocity increases because the available flow area decreases, and the pressure decreases as a result of the conservation of energy. Conversely, as the fluid flows around the back side of the body, the velocity decreases and the pressure increases. This is not unlike the flow in a diffuser or a converging-diverging duct. The flow behind the sphere into an adverse pressure gradient is inherently unstable, so as the velocity (and lVRe) increase it becomes more difficult for the streamlines to follow the contour of the body, and they eventually break away from the surface. This condition is called separation, although it is the smooth streamline that is separating from the surface, not the fluid itself. When separation occurs eddies or vortices form behind the body as illustrated in Fig. 11-1 and form a wake behind the sphere. 

Ret < 300 Unsteady laminar inertial flow in which laminar wake oscillations appear in the pores and vortices form at around Ret — 250 ... 

As Re increases, skin friction becomes proportionately less and, at values greater than about 20, flow separation occurs with the formation of vortices in the wake of the sphere. At high Reynolds numbers, the size of the vortices progressively increases until, at values of between 100 and 200, instabilities in the flow give rise to vortex shedding. The effect of these changes in the nature of the flow on the force exerted on the particle is now considered. 

At Re = 130, a weak long-period oscillation appears in the tip of the wake (T2). Its amplitude increases with Re, but the flow behind the attached wake remains laminar to Re above 200. The amplitude of oscillation at the tip reaches 10% of the sphere diameter at Re = 270 (GIO). At about this Re, large vortices, associated with pulsations of the fluid circulating in the wake, periodically form and move downstream (S6). Vortex shedding appears to result from flow instability, originating in the free surface layer and moving downstream to affect the position of the wake tip (Rll, R12, S6). 

The manatees leave a stream of lights in their wake that you find easy to follow. Occasionally you see vortices spiraling away from you, like miniature tornadoes. You stay away from them, just in case they are sufficiently strong to affect your motion. 

Leal, L. G. (1989). Vorticity Transport and Wake Structure for Bluff Bodies at Finite Reynolds Number. Phys. Fluids A, Fluid Dynamics, 1,124. 

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