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 - 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 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 - 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 - 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 - 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 - 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 - 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 -