TY - JOUR AB - Based on a novel control scheme, where a steady modification of the streamwise velocity profile leads to complete relaminarization of initially fully turbulent pipe flow, we investigate the applicability and usefulness of custom-shaped honeycombs for such control. The custom-shaped honeycombs are used as stationary flow management devices which generate specific modifications of the streamwise velocity profile. Stereoscopic particle image velocimetry and pressure drop measurements are used to investigate and capture the development of the relaminarizing flow downstream these devices. We compare the performance of straight (constant length across the radius of the pipe) honeycombs with custom-shaped ones (variable length across the radius) and try to determine the optimal shape for maximal relaminarization at minimal pressure loss. The optimally modified streamwise velocity profile is found to be M-shaped, and the maximum attainable Reynolds number for total relaminarization is found to be of the order of 10,000. Consequently, the respective reduction in skin friction downstream of the device is almost by a factor of 5. The break-even point, where the additional pressure drop caused by the device is balanced by the savings due to relaminarization and a net gain is obtained, corresponds to a downstream stretch of distances as low as approximately 100 pipe diameters of laminar flow. AU - Kühnen, Jakob AU - Scarselli, Davide AU - Hof, Björn ID - 6486 IS - 11 JF - Journal of Fluids Engineering SN - 00982202 TI - Relaminarization of pipe flow by means of 3D-printed shaped honeycombs VL - 141 ER - TY - JOUR AB - Following the recent observation that turbulent pipe flow can be relaminarised bya relatively simple modification of the mean velocity profile, we here carry out aquantitative experimental investigation of this phenomenon. Our study confirms thata flat velocity profile leads to a collapse of turbulence and in order to achieve theblunted profile shape, we employ a moving pipe segment that is briefly and rapidlyshifted in the streamwise direction. The relaminarisation threshold and the minimumshift length and speeds are determined as a function of Reynolds number. Althoughturbulence is still active after the acceleration phase, the modulated profile possessesa severely decreased lift-up potential as measured by transient growth. As shown,this results in an exponential decay of fluctuations and the flow relaminarises. Whilethis method can be easily applied at low to moderate flow speeds, the minimumstreamwise length over which the acceleration needs to act increases linearly with theReynolds number. AU - Scarselli, Davide AU - Kühnen, Jakob AU - Hof, Björn ID - 6228 JF - Journal of Fluid Mechanics SN - 00221120 TI - Relaminarising pipe flow by wall movement VL - 867 ER - TY - JOUR AB - Segregation of maternal determinants within the oocyte constitutes the first step in embryo patterning. In zebrafish oocytes, extensive ooplasmic streaming leads to the segregation of ooplasm from yolk granules along the animal-vegetal axis of the oocyte. Here, we show that this process does not rely on cortical actin reorganization, as previously thought, but instead on a cell-cycle-dependent bulk actin polymerization wave traveling from the animal to the vegetal pole of the oocyte. This wave functions in segregation by both pulling ooplasm animally and pushing yolk granules vegetally. Using biophysical experimentation and theory, we show that ooplasm pulling is mediated by bulk actin network flows exerting friction forces on the ooplasm, while yolk granule pushing is achieved by a mechanism closely resembling actin comet formation on yolk granules. Our study defines a novel role of cell-cycle-controlled bulk actin polymerization waves in oocyte polarization via ooplasmic segregation. AU - Shamipour, Shayan AU - Kardos, Roland AU - Xue, Shi-lei AU - Hof, Björn AU - Hannezo, Edouard B AU - Heisenberg, Carl-Philipp J ID - 6508 IS - 6 JF - Cell SN - 00928674 TI - Bulk actin dynamics drive phase segregation in zebrafish oocytes VL - 177 ER - TY - JOUR AU - Schwayer, Cornelia AU - Shamipour, Shayan AU - Pranjic-Ferscha, Kornelija AU - Schauer, Alexandra AU - Balda, M AU - Tada, M AU - Matter, K AU - Heisenberg, Carl-Philipp J ID - 7001 IS - 4 JF - Cell SN - 0092-8674 TI - Mechanosensation of tight junctions depends on ZO-1 phase separation and flow VL - 179 ER - TY - JOUR AB - Suspended particles can alter the properties of fluids and in particular also affect the transition fromlaminar to turbulent flow. An earlier study [Mataset al.,Phys. Rev. Lett.90, 014501 (2003)] reported howthe subcritical (i.e., hysteretic) transition to turbulent puffs is affected by the addition of particles. Here weshow that in addition to this known transition, with increasing concentration a supercritical (i.e.,continuous) transition to a globally fluctuating state is found. At the same time the Newtonian-typetransition to puffs is delayed to larger Reynolds numbers. At even higher concentration only the globallyfluctuating state is found. The dynamics of particle laden flows are hence determined by two competinginstabilities that give rise to three flow regimes: Newtonian-type turbulence at low, a particle inducedglobally fluctuating state at high, and a coexistence state at intermediate concentrations. AU - Agrawal, Nishchal AU - Choueiri, George H AU - Hof, Björn ID - 6189 IS - 11 JF - Physical Review Letters SN - 00319007 TI - Transition to turbulence in particle laden flows VL - 122 ER - TY - JOUR AB - Over the past decade, the edge of chaos has proven to be a fruitful starting point for investigations of shear flows when the laminar base flow is linearly stable. Numerous computational studies of shear flows demonstrated the existence of states that separate laminar and turbulent regions of the state space. In addition, some studies determined invariant solutions that reside on this edge. In this paper, we study the unstable manifold of one such solution with the aid of continuous symmetry reduction, which we formulate here for the simultaneous quotiening of axial and azimuthal symmetries. Upon our investigation of the unstable manifold, we discover a previously unknown traveling-wave solution on the laminar-turbulent boundary with a relatively complex structure. By means of low-dimensional projections, we visualize different dynamical paths that connect these solutions to the turbulence. Our numerical experiments demonstrate that the laminar-turbulent boundary exhibits qualitatively different regions whose properties are influenced by the nearby invariant solutions. AU - Budanur, Nazmi B AU - Hof, Björn ID - 291 IS - 5 JF - Physical Review Fluids TI - Complexity of the laminar-turbulent boundary in pipe flow VL - 3 ER - TY - JOUR AB - Creeping flow of polymeric fluid without inertia exhibits elastic instabilities and elastic turbulence accompanied by drag enhancement due to elastic stress produced by flow-stretched polymers. However, in inertia-dominated flow at high Re and low fluid elasticity El, a reduction in turbulent frictional drag is caused by an intricate competition between inertial and elastic stresses. Here we explore the effect of inertia on the stability of viscoelastic flow in a broad range of control parameters El and (Re,Wi). We present the stability diagram of observed flow regimes in Wi-Re coordinates and find that the instabilities' onsets show an unexpectedly nonmonotonic dependence on El. Further, three distinct regions in the diagram are identified based on El. Strikingly, for high-elasticity fluids we discover a complete relaminarization of flow at Reynolds number in the range of 1 to 10, different from a well-known turbulent drag reduction. These counterintuitive effects may be explained by a finite polymer extensibility and a suppression of vorticity at high Wi. Our results call for further theoretical and numerical development to uncover the role of inertial effect on elastic turbulence in a viscoelastic flow. AU - Varshney, Atul AU - Steinberg, Victor ID - 17 IS - 10 JF - Physical Review Fluids TI - Drag enhancement and drag reduction in viscoelastic flow VL - 3 ER - TY - JOUR AB - We report quantitative evidence of mixing-layer elastic instability in a viscoelastic fluid flow between two widely spaced obstacles hindering a channel flow at Re 1 and Wi 1. Two mixing layers with nonuniform shear velocity profiles are formed in the region between the obstacles. The mixing-layer instability arises in the vicinity of an inflection point on the shear velocity profile with a steep variation in the elastic stress. The instability results in an intermittent appearance of small vortices in the mixing layers and an amplification of spatiotemporal averaged vorticity in the elastic turbulence regime. The latter is characterized through scaling of friction factor with Wi and both pressure and velocity spectra. Furthermore, the observations reported provide improved understanding of the stability of the mixing layer in a viscoelastic fluid at large elasticity, i.e., Wi 1 and Re 1 and oppose the current view of suppression of vorticity solely by polymer additives. AU - Varshney, Atul AU - Steinberg, Victor ID - 16 IS - 10 JF - Physical Review Fluids TI - Mixing layer instability and vorticity amplification in a creeping viscoelastic flow VL - 3 ER - TY - JOUR AB - This study treats with the influence of a symmetry-breaking transversal magnetic field on the nonlinear dynamics of ferrofluidic Taylor-Couette flow – flow confined between two concentric independently rotating cylinders. We detected alternating ‘flip’ solutions which are flow states featuring typical characteristics of slow-fast-dynamics in dynamical systems. The flip corresponds to a temporal change in the axial wavenumber and we find them to appear either as pure 2-fold axisymmetric (due to the symmetry-breaking nature of the applied transversal magnetic field) or involving non-axisymmetric, helical modes in its interim solution. The latter ones show features of typical ribbon solutions. In any case the flip solutions have a preferential first axial wavenumber which corresponds to the more stable state (slow dynamics) and second axial wavenumber, corresponding to the short appearing more unstable state (fast dynamics). However, in both cases the flip time grows exponential with increasing the magnetic field strength before the flip solutions, living on 2-tori invariant manifolds, cease to exist, with lifetime going to infinity. Further we show that ferrofluidic flow turbulence differ from the classical, ordinary (usually at high Reynolds number) turbulence. The applied magnetic field hinders the free motion of ferrofluid partials and therefore smoothen typical turbulent quantities and features so that speaking of mildly chaotic dynamics seems to be a more appropriate expression for the observed motion. AU - Altmeyer, Sebastian ID - 519 JF - Journal of Magnetism and Magnetic Materials TI - Non-linear dynamics and alternating ‘flip’ solutions in ferrofluidic Taylor-Couette flow VL - 452 ER - TY - JOUR AB - In pipes, turbulence sets in despite the linear stability of the laminar Hagen–Poiseuille flow. The Reynolds number ( ) for which turbulence first appears in a given experiment – the ‘natural transition point’ – depends on imperfections of the set-up, or, more precisely, on the magnitude of finite amplitude perturbations. At onset, turbulence typically only occupies a certain fraction of the flow, and this fraction equally is found to differ from experiment to experiment. Despite these findings, Reynolds proposed that after sufficiently long times, flows may settle to steady conditions: below a critical velocity, flows should (regardless of initial conditions) always return to laminar, while above this velocity, eddying motion should persist. As will be shown, even in pipes several thousand diameters long, the spatio-temporal intermittent flow patterns observed at the end of the pipe strongly depend on the initial conditions, and there is no indication that different flow patterns would eventually settle to a (statistical) steady state. Exploiting the fact that turbulent puffs do not age (i.e. they are memoryless), we continuously recreate the puff sequence exiting the pipe at the pipe entrance, and in doing so introduce periodic boundary conditions for the puff pattern. This procedure allows us to study the evolution of the flow patterns for arbitrary long times, and we find that after times in excess of advective time units, indeed a statistical steady state is reached. Although the resulting flows remain spatio-temporally intermittent, puff splitting and decay rates eventually reach a balance, so that the turbulent fraction fluctuates around a well-defined level which only depends on . In accordance with Reynolds’ proposition, we find that at lower (here 2020), flows eventually always resume to laminar, while for higher ( ), turbulence persists. The critical point for pipe flow hence falls in the interval of $2020 , which is in very good agreement with the recently proposed value of . The latter estimate was based on single-puff statistics and entirely neglected puff interactions. Unlike in typical contact processes where such interactions strongly affect the percolation threshold, in pipe flow, the critical point is only marginally influenced. Interactions, on the other hand, are responsible for the approach to the statistical steady state. As shown, they strongly affect the resulting flow patterns, where they cause ‘puff clustering’, and these regions of large puff densities are observed to travel across the puff pattern in a wave-like fashion. AU - Vasudevan, Mukund AU - Hof, Björn ID - 5996 JF - Journal of Fluid Mechanics SN - 0022-1120 TI - The critical point of the transition to turbulence in pipe flow VL - 839 ER - TY - JOUR AB - The drag of turbulent flows can be drastically decreased by adding small amounts of high molecular weight polymers. While drag reduction initially increases with polymer concentration, it eventually saturates to what is known as the maximum drag reduction (MDR) asymptote; this asymptote is generally attributed to the dynamics being reduced to a marginal yet persistent state of subdued turbulent motion. Contrary to this accepted view, we show that, for an appropriate choice of parameters, polymers can reduce the drag beyond the suggested asymptotic limit, eliminating turbulence and giving way to laminar flow. At higher polymer concentrations, however, the laminar state becomes unstable, resulting in a fluctuating flow with the characteristic drag of the MDR asymptote. Our findings indicate that the asymptotic state is hence dynamically disconnected from ordinary turbulence. © 2018 American Physical Society. AU - Choueiri, George H AU - Lopez Alonso, Jose M AU - Hof, Björn ID - 328 IS - 12 JF - Physical Review Letters TI - Exceeding the asymptotic limit of polymer drag reduction VL - 120 ER - TY - JOUR AB - Recent studies suggest that unstable, nonchaotic solutions of the Navier-Stokes equation may provide deep insights into fluid turbulence. In this article, we present a combined experimental and numerical study exploring the dynamical role of unstable equilibrium solutions and their invariant manifolds in a weakly turbulent, electromagnetically driven, shallow fluid layer. Identifying instants when turbulent evolution slows down, we compute 31 unstable equilibria of a realistic two-dimensional model of the flow. We establish the dynamical relevance of these unstable equilibria by showing that they are closely visited by the turbulent flow. We also establish the dynamical relevance of unstable manifolds by verifying that they are shadowed by turbulent trajectories departing from the neighborhoods of unstable equilibria over large distances in state space. AU - Suri, Balachandra AU - Tithof, Jeffrey AU - Grigoriev, Roman AU - Schatz, Michael ID - 136 IS - 2 JF - Physical Review E TI - Unstable equilibria and invariant manifolds in quasi-two-dimensional Kolmogorov-like flow VL - 98 ER - TY - JOUR AB - We show that a rather simple, steady modification of the streamwise velocity profile in a pipe can lead to a complete collapse of turbulence and the flow fully relaminarizes. Two different devices, a stationary obstacle (inset) and a device which injects fluid through an annular gap close to the wall, are used to control the flow. Both devices modify the streamwise velocity profile such that the flow in the center of the pipe is decelerated and the flow in the near wall region is accelerated. We present measurements with stereoscopic particle image velocimetry to investigate and capture the development of the relaminarizing flow downstream these devices and the specific circumstances responsible for relaminarization. We find total relaminarization up to Reynolds numbers of 6000, where the skin friction in the far downstream distance is reduced by a factor of 3.4 due to relaminarization. In a smooth straight pipe the flow remains completely laminar downstream of the control. Furthermore, we show that transient (temporary) relaminarization in a spatially confined region right downstream the devices occurs also at much higher Reynolds numbers, accompanied by a significant local skin friction drag reduction. The underlying physical mechanism of relaminarization is attributed to a weakening of the near-wall turbulence production cycle. AU - Kühnen, Jakob AU - Scarselli, Davide AU - Schaner, Markus AU - Hof, Björn ID - 422 IS - 4 JF - Flow Turbulence and Combustion TI - Relaminarization by steady modification of the streamwise velocity profile in a pipe VL - 100 ER - TY - JOUR AB - 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, 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 measuring the interaction between eddies and the mean shear is found to set a threshold below which turbulence is suppressed beyond recovery. AU - Kühnen, Jakob AU - Song, Baofang AU - Scarselli, Davide AU - Budanur, Nazmi B AU - Riedl, Michael AU - Willis, Ashley AU - Avila, Marc AU - Hof, Björn ID - 461 JF - Nature Physics TI - Destabilizing turbulence in pipe flow VL - 14 ER - TY - JOUR AB - Systems such as fluid flows in channels and pipes or the complex Ginzburg–Landau system, defined over periodic domains, exhibit both continuous symmetries, translational and rotational, as well as discrete symmetries under spatial reflections or complex conjugation. The simplest, and very common symmetry of this type is the equivariance of the defining equations under the orthogonal group O(2). We formulate a novel symmetry reduction scheme for such systems by combining the method of slices with invariant polynomial methods, and show how it works by applying it to the Kuramoto–Sivashinsky system in one spatial dimension. As an example, we track a relative periodic orbit through a sequence of bifurcations to the onset of chaos. Within the symmetry-reduced state space we are able to compute and visualize the unstable manifolds of relative periodic orbits, their torus bifurcations, a transition to chaos via torus breakdown, and heteroclinic connections between various relative periodic orbits. It would be very hard to carry through such analysis in the full state space, without a symmetry reduction such as the one we present here. AU - Budanur, Nazmi B AU - Cvitanović, Predrag ID - 1211 IS - 3-4 JF - Journal of Statistical Physics TI - Unstable manifolds of relative periodic orbits in the symmetry reduced state space of the Kuramoto–Sivashinsky system VL - 167 ER - TY - JOUR AB - We present an experimental setup that creates a shear flow with zero mean advection velocity achieved by counterbalancing the nonzero streamwise pressure gradient by moving boundaries, which generates plane Couette-Poiseuille flow. We obtain experimental results in the transitional regime for this flow. Using flow visualization, we characterize the subcritical transition to turbulence in Couette-Poiseuille flow and show the existence of turbulent spots generated by a permanent perturbation. Due to the zero mean advection velocity of the base profile, these turbulent structures are nearly stationary. We distinguish two regions of the turbulent spot: the active turbulent core, which is characterized by waviness of the streaks similar to traveling waves, and the surrounding region, which includes in addition the weak undisturbed streaks and oblique waves at the laminar-turbulent interface. We also study the dependence of the size of these two regions on Reynolds number. Finally, we show that the traveling waves move in the downstream (Poiseuille) direction. AU - Klotz, Lukasz AU - Lemoult, Grégoire M AU - Frontczak, Idalia AU - Tuckerman, Laurette AU - Wesfreid, José ID - 513 IS - 4 JF - Physical Review Fluids TI - Couette-Poiseuille flow experiment with zero mean advection velocity: Subcritical transition to turbulence VL - 2 ER - TY - JOUR AB - Superhydrophobic surfaces reduce the frictional drag between water and solid materials, but this effect is often temporary. The realization of sustained drag reduction has applications for water vehicles and pipeline flows. AU - Hof, Björn ID - 651 IS - 7636 JF - Nature SN - 00280836 TI - Fluid dynamics: Water flows out of touch VL - 541 ER - TY - JOUR AB - We report a direct-numerical-simulation study of the Taylor-Couette flow in the quasi-Keplerian regime at shear Reynolds numbers up to (105). Quasi-Keplerian rotating flow has been investigated for decades as a simplified model system to study the origin of turbulence in accretion disks that is not fully understood. The flow in this study is axially periodic and thus the experimental end-wall effects on the stability of the flow are avoided. Using optimal linear perturbations as initial conditions, our simulations find no sustained turbulence: the strong initial perturbations distort the velocity profile and trigger turbulence that eventually decays. AU - Shi, Liang AU - Hof, Björn AU - Rampp, Markus AU - Avila, Marc ID - 662 IS - 4 JF - Physics of Fluids SN - 10706631 TI - Hydrodynamic turbulence in quasi Keplerian rotating flows VL - 29 ER - TY - JOUR AB - We investigate fundamental nonlinear dynamics of ferrofluidic Taylor-Couette flow - flow confined be-tween two concentric independently rotating cylinders - consider small aspect ratio by solving the ferro-hydrodynamical equations, carrying out systematic bifurcation analysis. Without magnetic field, we find steady flow patterns, previously observed with a simple fluid, such as those containing normal one- or two vortex cells, as well as anomalous one-cell and twin-cell flow states. However, when a symmetry-breaking transverse magnetic field is present, all flow states exhibit stimulated, finite two-fold mode. Various bifurcations between steady and unsteady states can occur, corresponding to the transitions between the two-cell and one-cell states. While unsteady, axially oscillating flow states can arise, we also detect the emergence of new unsteady flow states. In particular, we uncover two new states: one contains only the azimuthally oscillating solution in the configuration of the twin-cell flow state, and an-other a rotating flow state. Topologically, these flow states are a limit cycle and a quasiperiodic solution on a two-torus, respectively. Emergence of new flow states in addition to observed ones with classical fluid, indicates that richer but potentially more controllable dynamics in ferrofluidic flows, as such flow states depend on the external magnetic field. AU - Altmeyer, Sebastian AU - Do, Younghae AU - Lai, Ying ID - 1160 JF - Scientific Reports SN - 20452322 TI - Dynamics of ferrofluidic flow in the Taylor-Couette system with a small aspect ratio VL - 7 ER - TY - JOUR AB - Using extensive direct numerical simulations, the dynamics of laminar-turbulent fronts in pipe flow is investigated for Reynolds numbers between and 5500. We here investigate the physical distinction between the fronts of weak and strong slugs both by analysing the turbulent kinetic energy budget and by comparing the downstream front motion to the advection speed of bulk turbulent structures. Our study shows that weak downstream fronts travel slower than turbulent structures in the bulk and correspond to decaying turbulence at the front. At the downstream front speed becomes faster than the advection speed, marking the onset of strong fronts. In contrast to weak fronts, turbulent eddies are generated at strong fronts by feeding on the downstream laminar flow. Our study also suggests that temporal fluctuations of production and dissipation at the downstream laminar-turbulent front drive the dynamical switches between the two types of front observed up to. AU - Song, Baofang AU - Barkley, Dwight AU - Hof, Björn AU - Avila, Marc ID - 1087 JF - Journal of Fluid Mechanics SN - 00221120 TI - Speed and structure of turbulent fronts in pipe flow VL - 813 ER - TY - JOUR AB - Most flows in nature and engineering are turbulent because of their large velocities and spatial scales. Laboratory experiments on rotating quasi-Keplerian flows, for which the angular velocity decreases radially but the angular momentum increases, are however laminar at Reynolds numbers exceeding one million. This is in apparent contradiction to direct numerical simulations showing that in these experiments turbulence transition is triggered by the axial boundaries. We here show numerically that as the Reynolds number increases, turbulence becomes progressively confined to the boundary layers and the flow in the bulk fully relaminarizes. Our findings support that turbulence is unlikely to occur in isothermal constant-density quasi-Keplerian flows. AU - Lopez Alonso, Jose M AU - Avila, Marc ID - 1021 JF - Journal of Fluid Mechanics SN - 00221120 TI - Boundary layer turbulence in experiments on quasi Keplerian flows VL - 817 ER - TY - JOUR AB - The chaotic dynamics of low-dimensional systems, such as Lorenz or Rössler flows, is guided by the infinity of periodic orbits embedded in their strange attractors. Whether this is also the case for the infinite-dimensional dynamics of Navier–Stokes equations has long been speculated, and is a topic of ongoing study. Periodic and relative periodic solutions have been shown to be involved in transitions to turbulence. Their relevance to turbulent dynamics – specifically, whether periodic orbits play the same role in high-dimensional nonlinear systems like the Navier–Stokes equations as they do in lower-dimensional systems – is the focus of the present investigation. We perform here a detailed study of pipe flow relative periodic orbits with energies and mean dissipations close to turbulent values. We outline several approaches to reduction of the translational symmetry of the system. We study pipe flow in a minimal computational cell at Re=2500, and report a library of invariant solutions found with the aid of the method of slices. Detailed study of the unstable manifolds of a sample of these solutions is consistent with the picture that relative periodic orbits are embedded in the chaotic saddle and that they guide the turbulent dynamics. AU - Budanur, Nazmi B AU - Short, Kimberly AU - Farazmand, Mohammad AU - Willis, Ashley AU - Cvitanović, Predrag ID - 792 JF - Journal of Fluid Mechanics SN - 00221120 TI - Relative periodic orbits form the backbone of turbulent pipe flow VL - 833 ER - TY - JOUR AB - In shear flows at transitional Reynolds numbers, localized patches of turbulence, known as puffs, coexist with the laminar flow. Recently, Avila et al. (Phys. Rev. Lett., vol. 110, 2013, 224502) discovered two spatially localized relative periodic solutions for pipe flow, which appeared in a saddle-node bifurcation at low Reynolds number. Combining slicing methods for continuous symmetry reduction with Poincaré sections for the first time in a shear flow setting, we compute and visualize the unstable manifold of the lower-branch solution and show that it extends towards the neighbourhood of the upper-branch solution. Surprisingly, this connection even persists far above the bifurcation point and appears to mediate the first stage of the puff generation: amplification of streamwise localized fluctuations. When the state-space trajectories on the unstable manifold reach the vicinity of the upper branch, corresponding fluctuations expand in space and eventually take the usual shape of a puff. AU - Budanur, Nazmi B AU - Hof, Björn ID - 824 JF - Journal of Fluid Mechanics SN - 00221120 TI - Heteroclinic path to spatially localized chaos in pipe flow VL - 827 ER - TY - JOUR AB - Fluid flows in nature and applications are frequently subject to periodic velocity modulations. Surprisingly, even for the generic case of flow through a straight pipe, there is little consensus regarding the influence of pulsation on the transition threshold to turbulence: while most studies predict a monotonically increasing threshold with pulsation frequency (i.e. Womersley number, ), others observe a decreasing threshold for identical parameters and only observe an increasing threshold at low . In the present study we apply recent advances in the understanding of transition in steady shear flows to pulsating pipe flow. For moderate pulsation amplitudes we find that the first instability encountered is subcritical (i.e. requiring finite amplitude disturbances) and gives rise to localized patches of turbulence ('puffs') analogous to steady pipe flow. By monitoring the impact of pulsation on the lifetime of turbulence we map the onset of turbulence in parameter space. Transition in pulsatile flow can be separated into three regimes. At small Womersley numbers the dynamics is dominated by the decay turbulence suffers during the slower part of the cycle and hence transition is delayed significantly. As shown in this regime thresholds closely agree with estimates based on a quasi-steady flow assumption only taking puff decay rates into account. The transition point predicted in the zero limit equals to the critical point for steady pipe flow offset by the oscillation Reynolds number (i.e. the dimensionless oscillation amplitude). In the high frequency limit on the other hand, puff lifetimes are identical to those in steady pipe flow and hence the transition threshold appears to be unaffected by flow pulsation. In the intermediate frequency regime the transition threshold sharply drops (with increasing ) from the decay dominated (quasi-steady) threshold to the steady pipe flow level. AU - Xu, Duo AU - Warnecke, Sascha AU - Song, Baofang AU - Ma, Xingyu AU - Hof, Björn ID - 745 JF - Journal of Fluid Mechanics SN - 00221120 TI - Transition to turbulence in pulsating pipe flow VL - 831 ER - TY - JOUR AB - We present a numerical study of wavy supercritical cylindrical Couette flow between counter-rotating cylinders in which the wavy pattern propagates either prograde with the inner cylinder or retrograde opposite the rotation of the inner cylinder. The wave propagation reversals from prograde to retrograde and vice versa occur at distinct values of the inner cylinder Reynolds number when the associated frequency of the wavy instability vanishes. The reversal occurs for both twofold and threefold symmetric wavy vortices. Moreover, the wave propagation reversal only occurs for sufficiently strong counter-rotation. The flow pattern reversal appears to be intrinsic in the system as either periodic boundary conditions or fixed end wall boundary conditions for different system sizes always result in the wave propagation reversal. We present a detailed bifurcation sequence and parameter space diagram with respect to retrograde behavior of wavy flows. The retrograde propagation of the instability occurs when the inner Reynolds number is about two times the outer Reynolds number. The mechanism for the retrograde propagation is associated with the inviscidly unstable region near the inner cylinder and the direction of the global average azimuthal velocity. Flow dynamics, spatio-temporal behavior, global mean angular velocity, and torque of the flow with the wavy pattern are explored. AU - Altmeyer, Sebastian AU - Lueptow, Richard ID - 673 IS - 5 JF - Physical Review E SN - 2470-0045 TI - Wave propagation reversal for wavy vortices in wide gap counter rotating cylindrical Couette flow VL - 95 ER - TY - JOUR AB - We investigate transient behaviors induced by magnetic fields on the dynamics of the flow of a ferrofluid in the gap between two concentric, independently rotating cylinders. Without applying any magnetic fields, we uncover emergence of flow states constituted by a combination of a localized spiral state (SPIl) in the top and bottom of the annulus and different multi-cell flow states (SPI2v, SPI3v) with toroidally closed vortices in the interior of the bulk (SPIl+2v = SPIl + SPI2v and SPIl+3v = SPIl + SPI3v). However, when a magnetic field is presented, we observe the transient behaviors between multi-cell states passing through two critical thresholds in a strength of an axial (transverse) magnetic field. Before the first critical threshold of a magnetic field strength, multi-stable states with different number of cells could be observed. After the first critical threshold, we find the transient behavior between the three- and two-cell flow states. For more strength of magnetic field or after the second critical threshold, we discover that multi-cell states are disappeared and a localized spiral state remains to be stimulated. The studied transient behavior could be understood by the investigation of various quantities including a modal kinetic energy, a mode amplitude of the radial velocity, wavenumber, angular momentum, and torque. In addition, the emergence of new flow states and the transient behavior between their states in ferrofluidic flows indicate that richer and potentially controllable dynamics through magnetic fields could be possible in ferrofluic flow. AU - Altmeyer, Sebastian AU - Do, Younghae AU - Ryu, Soorok ID - 463 IS - 11 JF - Chaos SN - 10541500 TI - Transient behavior between multi-cell flow states in ferrofluidic Taylor-Couette flow VL - 27 ER - TY - JOUR AB - During embryonic development, mechanical forces are essential for cellular rearrangements driving tissue morphogenesis. Here, we show that in the early zebrafish embryo, friction forces are generated at the interface between anterior axial mesoderm (prechordal plate, ppl) progenitors migrating towards the animal pole and neurectoderm progenitors moving in the opposite direction towards the vegetal pole of the embryo. These friction forces lead to global rearrangement of cells within the neurectoderm and determine the position of the neural anlage. Using a combination of experiments and simulations, we show that this process depends on hydrodynamic coupling between neurectoderm and ppl as a result of E-cadherin-mediated adhesion between those tissues. Our data thus establish the emergence of friction forces at the interface between moving tissues as a critical force-generating process shaping the embryo. AU - Smutny, Michael AU - Ákos, Zsuzsa AU - Grigolon, Silvia AU - Shamipour, Shayan AU - Ruprecht, Verena AU - Capek, Daniel AU - Behrndt, Martin AU - Papusheva, Ekaterina AU - Tada, Masazumi AU - Hof, Björn AU - Vicsek, Tamás AU - Salbreux, Guillaume AU - Heisenberg, Carl-Philipp J ID - 661 JF - Nature Cell Biology SN - 14657392 TI - Friction forces position the neural anlage VL - 19 ER - TY - JOUR AB - Turbulence is one of the most frequently encountered non-equilibrium phenomena in nature, yet characterizing the transition that gives rise to turbulence in basic shear flows has remained an elusive task. Although, in recent studies, critical points marking the onset of sustained turbulence have been determined for several such flows, the physical nature of the transition could not be fully explained. In extensive experimental and computational studies we show for the example of Couette flow that the onset of turbulence is a second-order phase transition and falls into the directed percolation universality class. Consequently, the complex laminar–turbulent patterns distinctive for the onset of turbulence in shear flows result from short-range interactions of turbulent domains and are characterized by universal critical exponents. More generally, our study demonstrates that even high-dimensional systems far from equilibrium such as turbulence exhibit universality at onset and that here the collective dynamics obeys simple rules. AU - Lemoult, Grégoire M AU - Shi, Liang AU - Avila, Kerstin AU - Jalikop, Shreyas V AU - Avila, Marc AU - Hof, Björn ID - 1494 IS - 3 JF - Nature Physics TI - Directed percolation phase transition to sustained turbulence in Couette flow VL - 12 ER - TY - JOUR AB - We investigate the dynamics of ferrofluidic wavy vortex flows in the counter-rotating Taylor-Couette system, with a focus on wavy flows with a mixture of the dominant azimuthal modes. Without external magnetic field flows are stable and pro-grade with respect to the rotation of the inner cylinder. More complex behaviors can arise when an axial or a transverse magnetic field is applied. Depending on the direction and strength of the field, multi-stable wavy states and bifurcations can occur. We uncover the phenomenon of flow pattern reversal as the strength of the magnetic field is increased through a critical value. In between the regimes of pro-grade and retrograde flow rotations, standing waves with zero angular velocities can emerge. A striking finding is that, under a transverse magnetic field, a second reversal in the flow pattern direction can occur, where the flow pattern evolves into pro-grade rotation again from a retrograde state. Flow reversal is relevant to intriguing phenomena in nature such as geomagnetic reversal. Our results suggest that, in ferrofluids, flow pattern reversal can be induced by varying a magnetic field in a controlled manner, which can be realized in laboratory experiments with potential applications in the development of modern fluid devices. AU - Altmeyer, Sebastian AU - Do, Younghae AU - Lai, Ying ID - 1589 JF - Scientific Reports TI - Magnetic field induced flow pattern reversal in a ferrofluidic Taylor-Couette system VL - 5 ER - TY - JOUR AB - We investigate the Taylor-Couette system where the radius ratio is close to unity. Systematically increasing the Reynolds number, we observe a number of previously known transitions, such as one from the classical Taylor vortex flow (TVF) to wavy vortex flow (WVF) and the transition to fully developed turbulence. Prior to the onset of turbulence, we observe intermittent bursting patterns of localized turbulent patches, confirming the experimentally observed pattern of very short wavelength bursts (VSWBs). A striking finding is that, for a Reynolds number larger than that for the onset of VSWBs, a new type of intermittently bursting behavior emerges: patterns of azimuthally closed rings of various orders. We call them ring-bursting patterns, which surround the cylinder completely but remain localized and separated in the axial direction through nonturbulent wavy structures. We employ a number of quantitative measures including the cross-flow energy to characterize the ring-bursting patterns and to distinguish them from the background flow. These patterns are interesting because they do not occur in the wide-gap Taylor-Couette flow systems. The narrow-gap regime is less studied but certainly deserves further attention to gain deeper insights into complex flow dynamics in fluids. AU - Altmeyer, Sebastian AU - Do, Younghae AU - Lai, Ying ID - 1588 IS - 5 JF - Physical Review E TI - Ring-bursting behavior en route to turbulence in narrow-gap Taylor-Couette flows VL - 92 ER - TY - JOUR AB - Over a century of research into the origin of turbulence in wall-bounded shear flows has resulted in a puzzling picture in which turbulence appears in a variety of different states competing with laminar background flow. At moderate flow speeds, turbulence is confined to localized patches; it is only at higher speeds that the entire flow becomes turbulent. The origin of the different states encountered during this transition, the front dynamics of the turbulent regions and the transformation to full turbulence have yet to be explained. By combining experiments, theory and computer simulations, here we uncover a bifurcation scenario that explains the transformation to fully turbulent pipe flow and describe 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 and fully turbulent flows. AU - Barkley, Dwight AU - Song, Baofang AU - Vasudevan, Mukund AU - Lemoult, Grégoire M AU - Avila, Marc AU - Hof, Björn ID - 1664 IS - 7574 JF - Nature TI - The rise of fully turbulent flow VL - 526 ER - TY - JOUR AU - Lemoult, Grégoire M AU - Maier, Philipp AU - Hof, Björn ID - 1679 IS - 9 JF - Physics of Fluids TI - Taylor's Forest VL - 27 ER - TY - JOUR AB - It is known that in classical fluids turbulence typically occurs at high Reynolds numbers. But can turbulence occur at low Reynolds numbers? Here we investigate the transition to turbulence in the classic Taylor-Couette system in which the rotating fluids are manufactured ferrofluids with magnetized nanoparticles embedded in liquid carriers. We find that, in the presence of a magnetic field transverse to the symmetry axis of the system, turbulence can occur at Reynolds numbers that are at least one order of magnitude smaller than those in conventional fluids. This is established by extensive computational ferrohydrodynamics through a detailed investigation of transitions in the flow structure, and characterization of behaviors of physical quantities such as the energy, the wave number, and the angular momentum through the bifurcations. A finding is that, as the magnetic field is increased, onset of turbulence can be determined accurately and reliably. Our results imply that experimental investigation of turbulence may be feasible by using ferrofluids. Our study of transition to and evolution of turbulence in the Taylor-Couette ferrofluidic flow system provides insights into the challenging problem of turbulence control. AU - Altmeyer, Sebastian AU - Do, Younghae AU - Lai, Ying ID - 1804 JF - Scientific Reports TI - Transition to turbulence in Taylor-Couette ferrofluidic flow VL - 5 ER - TY - JOUR AB - Transition to turbulence in straight pipes occurs in spite of the linear stability of the laminar Hagen-Poiseuille flow if both the amplitude of flow perturbations and the Reynolds number Re exceed a minimum threshold (subcritical transition). As the pipe curvature increases, centrifugal effects become important, modifying the basic flow as well as the most unstable linear modes. If the curvature (tube-to-coiling diameter d/D) is sufficiently large, a Hopf bifurcation (supercritical instability) is encountered before turbulence can be excited (subcritical instability). We trace the instability thresholds in the Re - d/D parameter space in the range 0.01 ≤ d/D\ ≤ 0.1 by means of laser-Doppler velocimetry and determine the point where the subcritical and supercritical instabilities meet. Two different experimental set-ups are used: a closed system where the pipe forms an axisymmetric torus and an open system employing a helical pipe. Implications for the measurement of friction factors in curved pipes are discussed. AU - Kühnen, Jakob AU - Braunshier, P AU - Schwegel, M AU - Kuhlmann, Hendrik AU - Hof, Björn ID - 1837 IS - 5 JF - Journal of Fluid Mechanics TI - Subcritical versus supercritical transition to turbulence in curved pipes VL - 770 ER - TY - JOUR AB - We investigate high-dimensional nonlinear dynamical systems exhibiting multiple resonances under adiabatic parameter variations. Our motivations come from experimental considerations where time-dependent sweeping of parameters is a practical approach to probing and characterizing the bifurcations of the system. The question is whether bifurcations so detected are faithful representations of the bifurcations intrinsic to the original stationary system. Utilizing a harmonically forced, closed fluid flow system that possesses multiple resonances and solving the Navier-Stokes equation under proper boundary conditions, we uncover the phenomenon of the early effect. Specifically, as a control parameter, e.g., the driving frequency, is adiabatically increased from an initial value, resonances emerge at frequency values that are lower than those in the corresponding stationary system. The phenomenon is established by numerical characterization of physical quantities through the resonances, which include the kinetic energy and the vorticity field, and a heuristic analysis based on the concept of instantaneous frequency. A simple formula is obtained which relates the resonance points in the time-dependent and time-independent systems. Our findings suggest that, in general, any true bifurcation of a nonlinear dynamical system can be unequivocally uncovered through adiabatic parameter sweeping, in spite of a shift in the bifurcation point, which is of value to experimental studies of nonlinear dynamical systems. AU - Park, Youngyong AU - Do, Younghae AU - Altmeyer, Sebastian AU - Lai, Yingcheng AU - Lee, Gyuwon ID - 1868 IS - 2 JF - Physical Review E SN - 1539-3755 TI - Early effect in time-dependent, high-dimensional nonlinear dynamical systems with multiple resonances VL - 91 ER - TY - JOUR AB - A hybrid-parallel direct-numerical-simulation method with application to turbulent Taylor-Couette flow is presented. The Navier-Stokes equations are discretized in cylindrical coordinates with the spectral Fourier-Galerkin method in the axial and azimuthal directions, and high-order finite differences in the radial direction. Time is advanced by a second-order, semi-implicit projection scheme, which requires the solution of five Helmholtz/Poisson equations, avoids staggered grids and renders very small slip velocities. Nonlinear terms are evaluated with the pseudospectral method. The code is parallelized using a hybrid MPI-OpenMP strategy, which, compared with a flat MPI parallelization, is simpler to implement, allows to reduce inter-node communications and MPI overhead that become relevant at high processor-core counts, and helps to contain the memory footprint. A strong scaling study shows that the hybrid code maintains scalability up to more than 20,000 processor cores and thus allows to perform simulations at higher resolutions than previously feasible. In particular, it opens up the possibility to simulate turbulent Taylor-Couette flows at Reynolds numbers up to O(105). This enables to probe hydrodynamic turbulence in Keplerian flows in experimentally relevant regimes. AU - Shi, Liang AU - Rampp, Markus AU - Hof, Björn AU - Avila, Marc ID - 2030 IS - 1 JF - Computers and Fluids TI - A hybrid MPI-OpenMP parallel implementation for pseudospectral simulations with application to Taylor-Couette flow VL - 106 ER - TY - JOUR AB - The flow instability and further transition to turbulence in a toroidal pipe (torus) with curvature ratio (tube-to-coiling diameter) 0.049 is investigated experimentally. The flow inside the toroidal pipe is driven by a steel sphere fitted to the inner pipe diameter. The sphere is moved with constant azimuthal velocity from outside the torus by a moving magnet. The experiment is designed to investigate curved pipe flow by optical measurement techniques. Using stereoscopic particle image velocimetry, laser Doppler velocimetry and pressure drop measurements, the flow is measured for Reynolds numbers ranging from 1000 to 15 000. Time- and space-resolved velocity fields are obtained and analysed. The steady axisymmetric basic flow is strongly influenced by centrifugal effects. On an increase of the Reynolds number we find a sequence of bifurcations. For Re=4075±2% a supercritical bifurcation to an oscillatory flow is found in which waves travel in the streamwise direction with a phase velocity slightly faster than the mean flow. The oscillatory flow is superseded by a presumably quasi-periodic flow at a further increase of the Reynolds number before turbulence sets in. The results are found to be compatible, in general, with earlier experimental and numerical investigations on transition to turbulence in helical and curved pipes. However, important aspects of the bifurcation scenario differ considerably. AU - Kühnen, Jakob AU - Holzner, Markus AU - Hof, Björn AU - Kuhlmann, Hendrik ID - 2050 JF - Journal of Fluid Mechanics TI - Experimental investigation of transitional flow in a toroidal pipe VL - 738 ER - TY - JOUR AB - This work investigates the transition between different traveling helical waves (spirals, SPIs) in the setup of differentially independent rotating cylinders. We use direct numerical simulations to consider an infinite long and periodic Taylor-Couette apparatus with fixed axial periodicity length. We find so-called mixed-cross-spirals (MCSs), that can be seen as nonlinear superpositions of SPIs, to establish stable footbridges connecting SPI states. While bridging the bifurcation branches of SPIs, the corresponding contributions within the MCS vary continuously with the control parameters. Here discussed MCSs presenting footbridge solutions start and end in different SPI branches. Therefore they differ significantly from the already known MCSs that present bypass solutions (Altmeyer and Hoffmann 2010 New J. Phys. 12 113035). The latter start and end in the same SPI branch, while they always bifurcate out of those SPI branches with the larger mode amplitude. Meanwhile, these only appear within the coexisting region of both SPIs. In contrast, the footbridge solutions can also bifurcate out of the minor SPI contribution. We also find they exist in regions where only one of the SPIs contributions exists. In addition, MCS as footbridge solution can appear either stable or unstable. The latter detected transient solutions offer similar spatio-temporal characteristics to the flow establishing stable footbridges. Such transition processes are interesting for pattern-forming systems in general because they accomplish transitions between traveling waves of different azimuthal wave numbers and have not been described in the literature yet. AU - Altmeyer, Sebastian ID - 2224 IS - 2 JF - Fluid Dynamics Research SN - 01695983 TI - On secondary instabilities generating footbridges between spiral vortex flow VL - 46 ER - TY - JOUR AB - The purpose of this contribution is to summarize and discuss recent advances regarding the onset of turbulence in shear flows. The absence of a clear-cut instability mechanism, the spatio-temporal intermittent character and extremely long lived transients are some of the major difficulties encountered in these flows and have hindered progress towards understanding the transition process. We will show for the case of pipe flow that concepts from nonlinear dynamics and statistical physics can help to explain the onset of turbulence. In particular, the turbulent structures (puffs) observed close to onset are spatially localized chaotic transients and their lifetimes increase super-exponentially with Reynolds number. At the same time fluctuations of individual turbulent puffs can (although very rarely) lead to the nucleation of new puffs. The competition between these two stochastic processes gives rise to a non-equilibrium phase transition where turbulence changes from a super-transient to a sustained state. AU - Song, Baofang AU - Hof, Björn ID - 2232 IS - 2 JF - Journal of Statistical Mechanics Theory and Experiment SN - 17425468 TI - Deterministic and stochastic aspects of the transition to turbulence VL - 2014 ER - TY - JOUR AB - Coriolis force effects on shear flows are important in geophysical and astrophysical contexts. We report a study on the linear stability and the transient energy growth of the plane Couette flow with system rotation perpendicular to the shear direction. External rotation causes linear instability. At small rotation rates, the onset of linear instability scales inversely with the rotation rate and the optimal transient growth in the linearly stable region is slightly enhanced ∼Re2. The corresponding optimal initial perturbations are characterized by roll structures inclined in the streamwise direction and are twisted under external rotation. At large rotation rates, the transient growth is significantly inhibited and hence linear stability analysis is a reliable indicator for instability. AU - Shi, Liang AU - Hof, Björn AU - Tilgner, Andreas ID - 2226 IS - 1 JF - Physical Review E Statistical Nonlinear and Soft Matter Physics SN - 15393755 TI - Transient growth of Ekman-Couette flow VL - 89 ER - TY - JOUR AB - A novel Taylor-Couette system has been constructed for investigations of transitional as well as high Reynolds number turbulent flows in very large aspect ratios. The flexibility of the setup enables studies of a variety of problems regarding hydrodynamic instabilities and turbulence in rotating flows. The inner and outer cylinders and the top and bottom endplates can be rotated independently with rotation rates of up to 30 Hz, thereby covering five orders of magnitude in Reynolds numbers (Re = 101-106). The radius ratio can be easily changed, the highest realized one is η = 0.98 corresponding to an aspect ratio of 260 gap width in the vertical and 300 in the azimuthal direction. For η < 0.98 the aspect ratio can be dynamically changed during measurements and complete transparency in the radial direction over the full length of the cylinders is provided by the usage of a precision glass inner cylinder. The temperatures of both cylinders are controlled independently. Overall this apparatus combines an unmatched variety in geometry, rotation rates, and temperatures, which is provided by a sophisticated high-precision bearing system. Possible applications are accurate studies of the onset of turbulence and spatio-temporal intermittent flow patterns in very large domains, transport processes of turbulence at high Re, the stability of Keplerian flows for different boundary conditions, and studies of baroclinic instabilities. AU - Avila, Kerstin AU - Hof, Björn ID - 2806 IS - 6 JF - Review of Scientific Instruments TI - High-precision Taylor-Couette experiment to study subcritical transitions and the role of boundary conditions and size effects VL - 84 ER - TY - JOUR AB - In pipe, channel, and boundary layer flows turbulence first occurs intermittently in space and time: at moderate Reynolds numbers domains of disordered turbulent motion are separated by quiescent laminar regions. Based on direct numerical simulations of pipe flow we argue here that the spatial intermittency has its origin in a nearest neighbor interaction between turbulent regions. We further show that in this regime turbulent flows are intrinsically intermittent with a well-defined equilibrium turbulent fraction but without ever assuming a steady pattern. This transition scenario is analogous to that found in simple models such as coupled map lattices. The scaling observed implies that laminar intermissions of the turbulent flow will persist to arbitrarily large Reynolds numbers. AU - Avila, Marc AU - Hof, Björn ID - 2811 IS - 6 JF - Physical Review E TI - Nature of laminar-turbulence intermittency in shear flows VL - 87 ER - TY - JOUR AB - Turbulence is ubiquitous in nature, yet even for the case of ordinary Newtonian fluids like water, our understanding of this phenomenon is limited. Many liquids of practical importance are more complicated (e.g., blood, polymer melts, paints), however; they exhibit elastic as well as viscous characteristics, and the relation between stress and strain is nonlinear. We demonstrate here for a model system of such complex fluids that at high shear rates, turbulence is not simply modified as previously believed but is suppressed and replaced by a different type of disordered motion, elasto-inertial turbulence. Elasto-inertial turbulence is found to occur at much lower Reynolds numbers than Newtonian turbulence, and the dynamical properties differ significantly. The friction scaling observed coincides with the so-called "maximum drag reduction" asymptote, which is exhibited by a wide range of viscoelastic fluids. AU - Samanta, Devranjan AU - Dubief, Yves AU - Holzner, Markus AU - Schäfer, Christof AU - Morozov, Alexander AU - Wagner, Christian AU - Hof, Björn ID - 2813 IS - 26 JF - PNAS TI - Elasto-inertial turbulence VL - 110 ER - TY - JOUR AB - Laminar-turbulent intermittency is intrinsic to the transitional regime of a wide range of fluid flows including pipe, channel, boundary layer, and Couette flow. In the latter turbulent spots can grow and form continuous stripes, yet in the stripe-normal direction they remain interspersed by laminar fluid. We carry out direct numerical simulations in a long narrow domain and observe that individual turbulent stripes are transient. In agreement with recent observations in pipe flow, we find that turbulence becomes sustained at a distinct critical point once the spatial proliferation outweighs the inherent decaying process. By resolving the asymptotic size distributions close to criticality we can for the first time demonstrate scale invariance at the onset of turbulence. AU - Shi, Liang AU - Avila, Marc AU - Hof, Björn ID - 2829 IS - 20 JF - Physical Review Letters TI - Scale invariance at the onset of turbulence in couette flow VL - 110 ER - TY - JOUR AB - Although the equations governing fluid flow are well known, there are no analytical expressions that describe the complexity of turbulent motion. A recent proposition is that in analogy to low dimensional chaotic systems, turbulence is organized around unstable solutions of the governing equations which provide the building blocks of the disordered dynamics. We report the discovery of periodic solutions which just like intermittent turbulence are spatially localized and show that turbulent transients arise from one such solution branch. AU - Avila, Marc AU - Mellibovsky, Fernando AU - Roland, Nicolas AU - Hof, Björn ID - 2834 IS - 22 JF - Physical Review Letters TI - Streamwise-localized solutions at the onset of turbulence in pipe flow VL - 110 ER -