This manuscript is the original submission to Nature. The final (published) version can be accessed at http://www.nature.com/nature/journal/v526/n7574/full/nature15701.html 1 arXiv:1510.09143v1 [physics.flu-dyn] Oct 2015Over a century of research into the origin of turbulence in wallbounded shear flows has resulted in a puzzling picture in which turbulence appears in a variety of different states competing with laminar background flow. [1][2][3][4][5][6] At slightly higher speeds the situation changes distinctly and the entire flow is turbulent. Neither the origin of the different states encountered during transition, nor their front dynamics, let alone the transformation to full turbulence could be explained to date. Combining experiments, theory and computer simulations here we uncover the bifurcation scenario organising the route to fully turbulent pipe flow and explain the front dynamics of the different states encountered in the process. Key to resolving this problem is the interpretation of the flow as a bistable system with nonlinear propagation (advection) of turbulent fronts. These findings bridge the gap between our understanding of the onset of turbulence 7 and fully turbulent flows. 8,9 The sudden appearance of localised turbulent patches in an otherwise quiescent flow was first observed by Osborne Reynolds for pipe flow 1 and has since been found to be the starting point of turbulence in most shear flows. 2,4,[10][11][12][13][14][15] Curiously, in this regime it is impossible to maintain turbulence over extended regions as it automatically 16,17 reduces to patches of characteristic size, called puffs in pipe flow (see Fig. 1a). Puffs can decay, or else split and thereby multiply. Once the Reynolds number R > 2040 the splitting process outweighs decay, resulting in sustained disordered motion. 7 Although sustained, turbulence at these low R only consists of puffs surrounded by laminar flow (Fig. 1a) and cannot form larger clusters. 17,18 At larger flow rates, the situation is fundamentally different: once triggered, turbulence aggressively expands and eliminates all laminar motion (Fig. 1b). Fully turbulent flow is now the natural state of the system and only then do wallbounded shear flows have characteristic mean properties such as the Blasius or Prandtl-von Karman friction laws. 9 This rise of fully turbulent flow has remained unexplained despite the fact that this transformation occurs in virtually all shear flows and generally dominates the dynamics at sufficiently large Reynolds numbers.A classical diagnostic for the formation of turbulence 2-5, 19, 20 is the propagation speed of the In each case, the flow is initially seeded with localised turbulent patches and the subsequent evolution is visualised via space-time plots in a reference frame co-moving with structures. Colours indicate the value of u 2 r + u 2 θ . Further highlighting the distinction between cases, shown at the top are cross sections of instantaneous flow within the pipe. A 35D section is shown with the vertical direction str...
Turbulence is the major cause of friction losses in transport processes and it is responsible for a drastic drag increase in flows over bounding surfaces. While much effort is invested into developing ways to control and reduce turbulence intensities [1][2][3] , so far no methods exist to altogether eliminate turbulence if velocities are sufficiently large. We demonstrate for pipe flow that appropriate distortions to the velocity profile lead to a complete collapse of turbulence and subsequently friction losses are reduced by as much as 90%. Counterintuitively, the return to laminar motion is accomplished by initially increasing turbulence intensities or by transiently amplifying wall shear. Since neither the Reynolds number nor the shear stresses decrease (the latter often increase), these measures are not indicative of turbulence collapse. Instead, an amplification mechanism 4,5 measuring the interaction between eddies and the mean shear is found to set a threshold below which turbulence is suppressed beyond recovery.Flows through pipes and hydraulic networks are generally turbulent and the friction losses encountered in these flows are responsible for approximately 10% of the global electric energy consumption. Here turbulence causes a severe drag increase and consequently much larger forces are needed to maintain desired flow rates. In pipes, both laminar and turbulent states are stable (the former is believed to be linearly stable for all Reynolds number (Re) values; the latter is stable if Re > 2, 040 (ref. 6 )), but with increasing speed the laminar state becomes more and more susceptible to small disturbances. Hence, in practice most flows are turbulent at sufficiently large Re. While the stability of laminar flow has been studied in great detail, little attention has been paid to the susceptibility of turbulence, the general assumption being that once turbulence is established it is stable.Many turbulence control strategies have been put forward to reduce the drag encountered in shear flows [7][8][9][10][11][12][13][14][15][16][17] . Recent strategies employ feedback mechanisms to actively counter selected velocity components or vortices. Such methods usually require knowledge of the full turbulent velocity field. In computer simulations 7,8 , it could be demonstrated that under these ideal conditions, flows at a low Re number can even be relaminarized. In experiments, the required detailed manipulation of the time-dependent velocity field is, however, currently impossible to achieve. Other studies employ passive (for example, riblets) or active (oscillations or excitation of travelling waves) methods to interfere with the near-wall turbulence creation. Typically here drag reduction of 10 to 40% has been reported, but often the control cost is substantially higher than the gain, or a net gain can be achieved only in a narrow Re number regime.Instead of attempting to control or counter certain components of the complex fluctuating flow fields, we will show in the following that by appropriately dist...
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