Vorticity, relative change

Inflow or outflow can be specified using appropriate boundary conditions, although some characteristic problems are more easily implemented with one than the other. In any case, it is important to insure that the conditions specified are self-consistent. For example, inflow can be specified along the top boundary, by specifying the inflow velocity at V, as in figure (3). This in turn specifies a relative change in vorticity from to o ... 

The soot formation and its control was studied in an annular diffusion flame using laser diagnostics and hot wire anemometry [17, 18]. Air and fuel were independently acoustically forced. The forcing altered the mean and turbulent flow field and introduced coherent vortices into the flow. This allowed complete control of fuel injection into the incipient vortex shedding process. The experiments showed that soot formation in the flame was controlled by changing the timing of fuel injection relative to air vortex roll-up. When fuel was injected into a fully developed vortex, islands of unmixed fuel inside the air-vortex core led to... 

The seasonal and interannual variabilities of the main pycnocline are caused by the changes in the flux of the wind relative vorticity. 

Thus, the vorticity and temperature fields are governed by equations having the same basic form. When Pr is equal to 1, the equations have exactly the same form. Even in this case, however, the vorticity and temperature fields will not be identical because the boundary conditions on the two fields at the surface will not in general be identical. However, there will obviously be similarities between the two fields. Vorticity is generated in the flow by the action of viscosity due to the presence of the surface. The temperature differences arise in the flow because the surface is at a temperature which is different from the flowing fluid. Thus, Eq. (2.76) essentially describes the rate at which viscous effects spread into the fluid while Eq. (2.77) describes the rate at which the effects of the temperature changes at the surface spread into the fluid. It will be seen that the relative rates of spread depend on the value of the Prandtl number. 

While the virtual mass force accounts for the form drag on the particle due to relative acceleration between the particle and the surrounding fluid, the history term accounts for the corresponding viscous effects. Moreover, the history force originates from the unsteady diffusion of the vorticity around the particle so there is a delay in the boundary layer development as the relative velocity changes with time [96, 97, 22]. This means that when the relative velocity between the particle and the fluid varies, the vorticity present at the particle surface changes and the surrounding flow needs a flnite time to readapt to the new conditions. 

There are two proper explanations, one based on physical intuition and the other based on the principle of material objectivity. The latter is discussed in many books on continuum mechanics.19 Here, we content ourselves with the intuitive physical explanation. The basis of this is that contributions to the deviatoric stress cannot arise from rigid-body motions -whether solid-body translation or rotation. Only if adjacent fluid elements are in relative (nonrigid-body) motion can random molecular motions lead to a net transport of momentum. We shall see in the next paragraph that the rate-of-strain tensor relates to the rate of change of the length of a line element connecting two material points of the fluid (that is, to relative displacements of the material points), whereas the antisymmetric part of Vu, known as the vorticity tensor 12, is related to its rate of (rigid-body) rotation. Thus it follows that t must depend explicitly on E, but not on 12 ... 

Dauzere (Dl) produced solidified Benard cells in 1907 by quickly cooling a thin layer of melted beeswax undergoing convection. Performing similar experiments in 1912 (D3, D4), he noticed that if the beeswax was boiled with water beforehand, or better still with an alkaline solution, the entire character of the cells would change. The cells isolated themselves into colonies separated by relatively quiet areas, and these colonies were eventually reduced to single isolated vortices (tourbillons isol6s) (see Fig. 19) which, after 30 to 45 min. 

The equation of motion given by Maxey and Riley is valid provided that two Reynolds numbers based on the radius of the sphere are small compared to unity. The two Reynolds numbers are uqRIv and R uol(Lv), where uq is a velocity that is characteristic of the undisturbed fluid, wq is a velocity that is characteristic of the relative motion between the particle and the undisturbed fluid, and T is a characteristic length of the undisturbed flow. These conditions imply that the time required for a significant change in the relative velocity is large compared to the timescale for viscous diffusion, and that viscous diffusion remains the dominant mechanism for the transfer of vorticity away from the sphere. 

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