Finally in part c of the figure we show a turbulent flow corresponding to much

# Finally in part c of the figure we show a turbulent

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Finally, in part (c) of the figure we show a turbulent flow corresponding to much higher flow speed. We see that the paths followed by fluid parcels are now quite complicated and entangled indicating a high degree of mixing (in this case only of momentum). Such flows are three dimensional and time dependent, and very difficult to predict in detail. The most important single point to observe from the above figures and discussion is that as flow speed increases, details of the flow become more complicated and ultimately there is a “transition”
38 CHAPTER 2. SOME BACKGROUND: BASIC PHYSICS OF FLUIDS (a) (b) (c) C C C H H H Figure 2.19: Laminar and turbulent flow of water from a faucet; (a) steady laminar, (b) periodic, wavy laminar, (c) turbulent. from laminar to turbulent flow. Identification of turbulence as a class of fluid flow was first made by Leonardo da Vinci more than 500 years ago as indicated by his now famous sketches, one of which we present here in Fig. 2.20. In fact, da Vinci was evidently the first to use the word “turbulence” to describe this type of flow behavior. Despite this early recognition of turbulence, little formal investigation was Figure 2.20: da Vinci sketch depicting turbulent flow. carried out until the late 19 th Century when experimental facilities were first becoming sufficiently sophisticated to permit such studies. The work of Osbourne Reynolds in the 1880s and 1890s is still widely used today, and in some sense little progress has been made over the past 100 years. In Fig. 2.21 we display a rendition of Reynolds’ original experiments that indicated in a semi-quantitative way the transition to turbulence of flow in a pipe as the flow speed is increased. What is evident from this figure is analogous to what we have already seen with flow from a faucet, but now in the context of an actual experiment; namely, as long as the flow speed is low the flow will be laminar, but as soon as it is fast enough turbulent flow will occur. Details as to how and why this happens are not completely understood and still constitute a major area of research in fluid dynamics, despite the fact that the problem has been recognized for five centuries and has been the subject of intense investigation for the past 120 years.
2.4. CLASSIFICATION OF FLOW PHENOMENA 39 (b) (a) glass pipe dye streak Figure 2.21: Reynolds’ experiment using water in a pipe to study transition to turbulence; (a) low-speed flow, (b) higher-speed flow. A transition similar to that seen in the Reynolds expriments can also take place as flow evolves spatially, as indicated in Fig. 2.22 (and also in da Vinci’s sketch). As the flow moves from left to laminar transitional turbulent Figure 2.22: Transition to turbulence in spatially-evolving flow. right we see the path of the dye streak become more complicated and irregular as transition begins.

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