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 indicatinga high degree of mixing (in this case only of momentum). Such flows are three dimensional andtime dependent, and very difficult to predict in detail.The most important single point to observe from the above figures and discussion is that as flowspeed increases, details of the flow become more complicated and ultimately there is a “transition”
38CHAPTER 2. SOME BACKGROUND: BASIC PHYSICS OF FLUIDS(a)(b)(c)CCCHHHFigure 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 morethan 500 years ago as indicated by his now famous sketches, one of which we present here inFig. 2.20. In fact, da Vinci was evidently the first to use the word “turbulence” to describe thistype of flow behavior. Despite this early recognition of turbulence, little formal investigation wasFigure 2.20: da Vinci sketch depicting turbulent flow.carried out until the late 19thCentury when experimental facilities were first becoming sufficientlysophisticated to permit such studies. The work of Osbourne Reynolds in the 1880s and 1890s is stillwidely 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-quantitativeway the transition to turbulence of flow in a pipe as the flow speed is increased. What is evidentfrom this figure is analogous to what we have already seen with flow from a faucet, but now inthe context of an actual experiment; namely, as long as the flow speed is low the flow will belaminar, but as soon as it is fast enough turbulent flow will occur.Details as to how and whythis happens are not completely understood and still constitute a major area of research in fluiddynamics, despite the fact that the problem has been recognized for five centuries and has beenthe subject of intense investigation for the past 120 years.
2.4. CLASSIFICATION OF FLOW PHENOMENA39(b)(a)glass pipedye streakFigure 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 evolvesspatially, as indicated in Fig. 2.22 (and also in da Vinci’s sketch). As the flow moves from left tolaminartransitionalturbulentFigure 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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