@article{5996, abstract = {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.}, author = {Vasudevan, Mukund and Hof, Björn}, issn = {1469-7645}, journal = {Journal of Fluid Mechanics}, pages = {76--94}, publisher = {Cambridge University Press}, title = {{The critical point of the transition to turbulence in pipe flow}}, doi = {10.1017/jfm.2017.923}, volume = {839}, year = {2018}, } @article{16, abstract = {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.}, author = {Varshney, Atul and Steinberg, Victor}, journal = {Physical Review Fluids}, number = {10}, publisher = {American Physical Society}, title = {{Mixing layer instability and vorticity amplification in a creeping viscoelastic flow}}, doi = {10.1103/PhysRevFluids.3.103303}, volume = {3}, year = {2018}, } @article{136, abstract = {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.}, author = {Suri, Balachandra and Tithof, Jeffrey and Grigoriev, Roman and Schatz, Michael}, journal = {Physical Review E}, number = {2}, publisher = {American Physical Society}, title = {{Unstable equilibria and invariant manifolds in quasi-two-dimensional Kolmogorov-like flow}}, doi = {10.1103/PhysRevE.98.023105}, volume = {98}, year = {2018}, } @article{422, abstract = {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.}, author = {Kühnen, Jakob and Scarselli, Davide and Schaner, Markus and Hof, Björn}, journal = {Flow Turbulence and Combustion}, number = {4}, pages = {919 -- 942}, publisher = {Springer}, title = {{Relaminarization by steady modification of the streamwise velocity profile in a pipe}}, doi = {10.1007/s10494-018-9896-4}, volume = {100}, year = {2018}, } @article{1087, abstract = {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.}, author = {Song, Baofang and Barkley, Dwight and Hof, Björn and Avila, Marc}, issn = {00221120}, journal = {Journal of Fluid Mechanics}, pages = {1045 -- 1059}, publisher = {Cambridge University Press}, title = {{Speed and structure of turbulent fronts in pipe flow}}, doi = {10.1017/jfm.2017.14}, volume = {813}, year = {2017}, } @article{1160, abstract = {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.}, author = {Altmeyer, Sebastian and Do, Younghae and Lai, Ying}, issn = {20452322}, journal = {Scientific Reports}, publisher = {Nature Publishing Group}, title = {{Dynamics of ferrofluidic flow in the Taylor-Couette system with a small aspect ratio}}, doi = {10.1038/srep40012}, volume = {7}, year = {2017}, } @article{792, abstract = {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.}, author = {Budanur, Nazmi B and Short, Kimberly and Farazmand, Mohammad and Willis, Ashley and Cvitanović, Predrag}, issn = {00221120}, journal = {Journal of Fluid Mechanics}, pages = {274 -- 301}, publisher = {Cambridge University Press}, title = {{Relative periodic orbits form the backbone of turbulent pipe flow}}, doi = {10.1017/jfm.2017.699}, volume = {833}, year = {2017}, } @article{824, abstract = {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.}, author = {Budanur, Nazmi B and Hof, Björn}, issn = {00221120}, journal = {Journal of Fluid Mechanics}, publisher = {Cambridge University Press}, title = {{Heteroclinic path to spatially localized chaos in pipe flow}}, doi = {10.1017/jfm.2017.516}, volume = {827}, year = {2017}, } @article{662, abstract = {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.}, author = {Shi, Liang and Hof, Björn and Rampp, Markus and Avila, Marc}, issn = {10706631}, journal = {Physics of Fluids}, number = {4}, publisher = {American Institute of Physics}, title = {{Hydrodynamic turbulence in quasi Keplerian rotating flows}}, doi = {10.1063/1.4981525}, volume = {29}, year = {2017}, } @article{673, abstract = {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.}, author = {Altmeyer, Sebastian and Lueptow, Richard}, issn = {2470-0045}, journal = {Physical Review E}, number = {5}, publisher = {American Physical Society}, title = {{Wave propagation reversal for wavy vortices in wide gap counter rotating cylindrical Couette flow}}, doi = {10.1103/PhysRevE.95.053103}, volume = {95}, year = {2017}, } @article{745, abstract = {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.}, author = {Xu, Duo and Warnecke, Sascha and Song, Baofang and Ma, Xingyu and Hof, Björn}, issn = {00221120}, journal = {Journal of Fluid Mechanics}, pages = {418 -- 432}, publisher = {Cambridge University Press}, title = {{Transition to turbulence in pulsating pipe flow}}, doi = {10.1017/jfm.2017.620}, volume = {831}, year = {2017}, } @article{463, abstract = {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.}, author = {Altmeyer, Sebastian and Do, Younghae and Ryu, Soorok}, issn = {10541500}, journal = {Chaos}, number = {11}, publisher = {AIP Publishing}, title = {{Transient behavior between multi-cell flow states in ferrofluidic Taylor-Couette flow}}, doi = {10.1063/1.5002771}, volume = {27}, year = {2017}, } @article{513, abstract = {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.}, author = {Klotz, Lukasz and Lemoult, Grégoire M and Frontczak, Idalia and Tuckerman, Laurette and Wesfreid, José}, journal = {Physical Review Fluids}, number = {4}, publisher = {American Physical Society}, title = {{Couette-Poiseuille flow experiment with zero mean advection velocity: Subcritical transition to turbulence}}, doi = {10.1103/PhysRevFluids.2.043904}, volume = {2}, year = {2017}, } @article{651, abstract = {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. }, author = {Hof, Björn}, issn = {00280836}, journal = {Nature}, number = {7636}, pages = {161 -- 162}, publisher = {Nature Publishing Group}, title = {{Fluid dynamics: Water flows out of touch}}, doi = {10.1038/541161a}, volume = {541}, year = {2017}, } @article{661, abstract = {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.}, author = {Smutny, Michael and Ákos, Zsuzsa and Grigolon, Silvia and Shamipour, Shayan and Ruprecht, Verena and Capek, Daniel and Behrndt, Martin and Papusheva, Ekaterina and Tada, Masazumi and Hof, Björn and Vicsek, Tamás and Salbreux, Guillaume and Heisenberg, Carl-Philipp J}, issn = {14657392}, journal = {Nature Cell Biology}, pages = {306 -- 317}, publisher = {Nature Publishing Group}, title = {{Friction forces position the neural anlage}}, doi = {10.1038/ncb3492}, volume = {19}, year = {2017}, } @article{1021, abstract = {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.}, author = {Lopez Alonso, Jose M and Avila, Marc}, issn = {00221120}, journal = {Journal of Fluid Mechanics}, pages = {21 -- 34}, publisher = {Cambridge University Press}, title = {{Boundary layer turbulence in experiments on quasi Keplerian flows}}, doi = {10.1017/jfm.2017.109}, volume = {817}, year = {2017}, } @article{1211, abstract = {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.}, author = {Budanur, Nazmi B and Cvitanović, Predrag}, journal = {Journal of Statistical Physics}, number = {3-4}, pages = {636--655}, publisher = {Springer}, title = {{Unstable manifolds of relative periodic orbits in the symmetry reduced state space of the Kuramoto–Sivashinsky system}}, doi = {10.1007/s10955-016-1672-z}, volume = {167}, year = {2017}, } @article{1494, abstract = {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.}, author = {Lemoult, Grégoire M and Shi, Liang and Avila, Kerstin and Jalikop, Shreyas V and Avila, Marc and Hof, Björn}, journal = {Nature Physics}, number = {3}, pages = {254 -- 258}, publisher = {Nature Publishing Group}, title = {{Directed percolation phase transition to sustained turbulence in Couette flow}}, doi = {10.1038/nphys3675}, volume = {12}, year = {2016}, } @article{1664, abstract = {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.}, author = {Barkley, Dwight and Song, Baofang and Vasudevan, Mukund and Lemoult, Grégoire M and Avila, Marc and Hof, Björn}, journal = {Nature}, number = {7574}, pages = {550 -- 553}, publisher = {Nature Publishing Group}, title = {{The rise of fully turbulent flow}}, doi = {10.1038/nature15701}, volume = {526}, year = {2015}, } @article{1679, author = {Lemoult, Grégoire M and Maier, Philipp and Hof, Björn}, journal = {Physics of Fluids}, number = {9}, publisher = {American Institute of Physics}, title = {{Taylor's Forest}}, doi = {10.1063/1.4930850}, volume = {27}, year = {2015}, }