Law of the wake

Mean Velocity Characteristics for Constant Fluid Properties. Mean velocity distributions measured in turbulent boundary layers when the fluid properties are uniform (low speeds and small temperature differences between the free stream and surface) are described in the reviews of Refs. 78 and 79. At a given station, the turbulent boundary layer is composed of two regions with velocity profiles described by the law of the wall and the law of the wake after Coles [80, 81]. 

FIGURE 632 Velocity decrement for an incompressible turbulent boundary layer away from the surface ( law of the wake ) [83],... 

FIGURE 633 Coles law of the wake function in The value of ft recommended in regions of zero or posi-Eq. 6.149 [81]. tive pressure gradients is... 

Reynolds number Ree. The correlated data are shown in Fig. 6.50, where the increase in the skin friction is plotted versus a parameter that accounts for both the intensity and the scale of the free-stream turbulence. The effect of free-stream turbulence is primarily in the outer region of the boundary layer, where the law of the wake is modified, and, hence, the boundary layer integral thicknesses are modified. 

Coles, D.E. (1956). The law of the wake in the turbulent bormdary layer. Journal of Fluid Mechanics 1 191-226. 

If the crack is considered to be a wake zone and p = p(u, t) in Eqns. (19) and (21) then, for a stationary crack, both the crack shape and Keff are time dependent, given respectively by u(x,t) and KejAt) from Eqns. (19) and (21) for the case of partial shielding. Cox and Rose35 recently considered an elastic time-dependent bridging law of the form... 

In trying to imagine this meeting of universes, we should abandon the idea of a localized explosion and imagine, instead, a universe whose physical laws suddenly cease to operate—as matter and antimatter achieve simultaneous, ubiquitous cancellation—leaving, in the wake of the closure... 

I say that It touches a man that his blood is sea vrater and bis tears are salt, that the seed of his loins is scarcely different from the same cells in a seaweed, and that of the stuff like his bones are coral made. I say that physical and biologic law lies down with him, and wakes when a child stirs in the womb, and that the sap in a tree, upnishing in the spring, and the smell of the loam, where the bacteria bestir themselves in darkness, and the path of the sun in the heaven, these are feels of first importance to his mental conclusions, and that a man who goes in no consciousness of them is a drifter and a dreamer, without a home or any contact with reality. ... 

Zeng et al. [3] used a force balance approach to predict the bubble diameter at departure. They included the surface tension, inertial force, buoyancy and the lift force created by the wake of the previously departed bubble. But there was empiricism involved in computing the inertial and drag forces. The study assumed a power law profile for growth rate with the proportionality constant exponent determined from the experiments. 

Lee [86] examined earlier studies on cylinders in turbulent flow fields, and found in turbulent flow that the wake would decrease with increasing turbulence intensity, and then disappear, and the mean flow would behave in the same manner as for Stokes flow. He therefore proposed, and showed, that the drag on a particle in turbulent flow could be determined from a Stokes law with the molecular viscosity replaced by an effective viscosity calculated from the volumetric concentration of particles, the flow Reynolds number, the density ratio, and the Proude number. The Proude number, determining the ratio between the initial- and gravity forces, is defined as ... 

Kolev [46] discussed the validity of these relations for fluid particle collisions considering the obvious discrepancies resulting from the different nature of the fluid particle collisions compared with the random molecular collisions. The basic assumptions in kinetic theory that the molecules are hard spheres and that the collisions are perfectly elastic and obey the classical conservation laws do not hold for real fluid particles because these particles are deformable, elastic and may agglomerate or even coalescence after random collisions. The collision density is thus not really an independent function of the coalescence probability. For bubbly flow Colella et al [15] also found the basic kinetic theory assumption that the particles are interacting only during collision violated, as the bubbles influence each other by means of their wakes. 

The boundary layer equations are valid only in the region between the front stagnation point and the separation point. Behind the separation point there is a wake region with absolutely different hydrodynamic laws. The position of the separation point can be determined either experimentally or by using numerical or approximate analytical methods. 

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