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Tham khảo tài liệu 'a heat transfer textbook - third edition episode 2 part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 314 Laminar and turbulent boundary layers 6.7 one or two enormous vortices of continental proportions. These huge vortices in turn feed smaller weather-making vortices on the order of hundreds of miles in diameter. These further dissipate into vortices of cyclone and tornado proportions sometimes with that level of violence but more often not. These dissipate into still smaller whirls as they interact with the ground and its various protrusions. The next time the wind blows stand behind any tree and feel the vortices. In the great plains where there are not many ground vortex generators such as trees you will see small cyclonic eddies called dust devils. The process continues right on down to millimeter or even micrometer scales. There momentum exchange is no longer identifiable as turbulence but appears simply as viscous stretching of the fluid. The same kind of process exists within say a turbulent pipe flow at high Reynolds number. Such a flow is shown in Fig. 6.17. Turbulence in such a case consists of coexisting vortices which vary in size from a substantial fraction of the pipe radius down to micrometer dimensions. The spectrum of sizes varies with location in the pipe. The size and intensity of vortices at the wall must clearly approach zero since the fluid velocity goes to zero at the wall. Figure 6.17 shows the fluctuation of a typical flow variable namely velocity both with location in the pipe and with time. This fluctuation arises because of the turbulent motions that are superposed on the average local flow. Other flow variables such as T or p can vary in the same manner. For any variable we can write a local time-average value as u 1 udt 6.81 T 0 where T is a time that is much longer than the period of typical fluctua-tions.9 Equation 6.81 is most useful for so-called stationary processes ones for which u is nearly time-independent. If we substitute u u u in eqn. 6.81 where u is the actual local velocity and u is the instantaneous magnitude of the .
