Surface vorticity distribution

Figure 5.24 shows predicted surface vorticity distributions at Re = 100 and for K = 0 (gas bubble), k = 1 (liquid drop in liquid of equal viscosity), and K = 55 (water drop in air), and for a rigid sphere. The results for the raindrop are very close to those for a rigid sphere. The bubble shows much lower surface vorticity due to higher velocity at the interface, while the k = 1 drop is intermediate. The absence of separation for the bubble and k = 1 drop is indicated by the fact that vorticity does not change sign. 

The viscous shearing at the stagnation surface is a source of vorticity that is transported into the flow. One way to characterize the boundary layer is in terms of its vorticity distribution. By definition, the circumferential component of the vorticity vector is given as... 

By making substitutions, the following expression for the vorticity distribution along the flame surface can be deduced ... 

FIGURE 5.4 Vorticity distribution at surface of fluid sphere for Re = 300 [15],... 

Form drag and skin friction drag coefficients are obtained from the numerical results by integrating the distributions of surface pressure and vorticity ... 

For case studies that compare model results with in situ observations we apply a nudging technique to ECHAM. At each time step ECHAM is relaxed towards ECMWF analyzed distributions of surface pressure, vorticity, divergence and temperature [35]. This enables the simulation of realistic meteorological situations so that simulated distributions of chemical species can be directly compared with measurement data for a specific time and place, thus... 

Figure 3.9. Zonally averaged distribution of the modified potential vorticity (unbroken lines in 10-4K m2s-1kg-1) from the surface to approximately 30 km altitude (10 hPa). The potential temperature (K) is represented by dashed lines and the tropopause by a dotted line. From Appenzeller (1994).

Figure 3.10. Global distribution of the potential vorticity on the 850 K isentropic surface during a wintertime planetary wave event. The shaded region over the Pacific ocean with a weak gradient is characterized by nonlinear wave dissipation and strong quasi-horizontal mixing. This region is referred to as the surf zone . Wind vectors are also indicated and provide information about large-scale transport. Courtesy of A. O Neill, University of Reading, UK.

A closer analysis of this problem would reveal more complex situations, such as a fluid flowing around a solid body. In that case the streamlines may take off behind the body at the limit of zero viscosity of the fluid. However, all fluids exhibit some viscosity and no such phenomenon can be observed. Experiments show that vorticity is generally generated in a thin boundary layer, close to a solid surface. It is propagated from the wall by both viscous diffusion and convection. The vortices are transported with the fluid they are observable for some time after their appearance. If the experiment is made with a circular cylinder moving at a constant velocity, the eddies appear in the wake of the body and their regular distribution constitutes the famous, as well as beautiful, Karman vortex street . 

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