TY - JOUR AB - It may come as a surprise that a phenomenon as ubiquitous and prominent as the transition from laminar to turbulent flow has resisted combined efforts by physicists, engineers and mathematicians, and remained unresolved for almost one and a half centuries. In recent years, various studies have proposed analogies to directed percolation, a well-known universality class in statistical mechanics, which describes a non-equilibrium phase transition from a fluctuating active phase into an absorbing state. It is this unlikely relation between the multiscale, high-dimensional dynamics that signify the transition process in virtually all flows of practical relevance, and the arguably most basic non-equilibrium phase transition, that so far has mainly been the subject of model studies, which I review in this Perspective. AU - Hof, Björn ID - 12165 JF - Nature Reviews Physics KW - General Physics and Astronomy TI - Directed percolation and the transition to turbulence VL - 5 ER - TY - JOUR AB - Data-driven dimensionality reduction methods such as proper orthogonal decomposition and dynamic mode decomposition have proven to be useful for exploring complex phenomena within fluid dynamics and beyond. A well-known challenge for these techniques is posed by the continuous symmetries, e.g. translations and rotations, of the system under consideration, as drifts in the data dominate the modal expansions without providing an insight into the dynamics of the problem. In the present study, we address this issue for fluid flows in rectangular channels by formulating a continuous symmetry reduction method that eliminates the translations in the streamwise and spanwise directions simultaneously. We demonstrate our method by computing the symmetry-reduced dynamic mode decomposition (SRDMD) of sliding windows of data obtained from the transitional plane-Couette and turbulent plane-Poiseuille flow simulations. In the former setting, SRDMD captures the dynamics in the vicinity of the invariant solutions with translation symmetries, i.e. travelling waves and relative periodic orbits, whereas in the latter, our calculations reveal episodes of turbulent time evolution that can be approximated by a low-dimensional linear expansion. AU - Marensi, Elena AU - Yalniz, Gökhan AU - Hof, Björn AU - Budanur, Nazmi B ID - 12105 JF - Journal of Fluid Mechanics SN - 0022-1120 TI - Symmetry-reduced dynamic mode decomposition of near-wall turbulence VL - 954 ER - TY - JOUR AB - The dissolution of minute concentration of polymers in wall-bounded flows is well-known for its unparalleled ability to reduce turbulent friction drag. Another phenomenon, elasto-inertial turbulence (EIT), has been far less studied even though elastic instabilities have already been observed in dilute polymer solutions before the discovery of polymer drag reduction. EIT is a chaotic state driven by polymer dynamics that is observed across many orders of magnitude in Reynolds number. It involves energy transfer from small elastic scales to large flow scales. The investigation of the mechanisms of EIT offers the possibility to better understand other complex phenomena such as elastic turbulence and maximum drag reduction. In this review, we survey recent research efforts that are advancing the understanding of the dynamics of EIT. We highlight the fundamental differences between EIT and Newtonian/inertial turbulence from the perspective of experiments, numerical simulations, instabilities, and coherent structures. Finally, we discuss the possible links between EIT and elastic turbulence and polymer drag reduction, as well as the remaining challenges in unraveling the self-sustaining mechanism of EIT. AU - Dubief, Yves AU - Terrapon, Vincent E. AU - Hof, Björn ID - 12681 IS - 1 JF - Annual Review of Fluid Mechanics SN - 0066-4189 TI - Elasto-inertial turbulence VL - 55 ER - TY - JOUR AB - Since the seminal studies by Osborne Reynolds in the nineteenth century, pipe flow has served as a primary prototype for investigating the transition to turbulence in wall-bounded flows. Despite the apparent simplicity of this flow, various facets of this problem have occupied researchers for more than a century. Here we review insights from three distinct perspectives: (a) stability and susceptibility of laminar flow, (b) phase transition and spatiotemporal dynamics, and (c) dynamical systems analysis of the Navier—Stokes equations. We show how these perspectives have led to a profound understanding of the onset of turbulence in pipe flow. Outstanding open points, applications to flows of complex fluids, and similarities with other wall-bounded flows are discussed. AU - Avila, Marc AU - Barkley, Dwight AU - Hof, Björn ID - 12682 JF - Annual Review of Fluid Mechanics SN - 0066-4189 TI - Transition to turbulence in pipe flow VL - 55 ER - TY - JOUR AB - In industrial reactors and equipment, non-ideality is quite a common phenomenon rather than an exception. These deviations from ideality impact the process's overall efficiency and the effectiveness of the equipment. To recognize the associated non-ideality, one needs to have enough understanding of the formulation of the equations and in-depth knowledge of the residence time distribution (RTD) data of real reactors. In the current work, step input and pulse input were used to create RTD data for Cascade continuous stirred tank reactors (CSTRs). For the aforementioned configuration, experiments were run at various flow rates to validate the developed characteristic equations. To produce RTD data, distilled water was utilized as the flowing fluid, and NaOH was the tracer substance. The ideal behavior of tracer concentration exits age distribution, and cumulative fraction for each setup and each input was plotted and experimental results were compared with perfect behavior. Deviation of concentration exit age distribution and cumulative fractional distribution from ideal behavior is more in pulse input as compared to a step input. For ideal cases, the exit age distribution curve and cumulative fraction curves are independent of the type of input. But a significant difference was observed for the two cases, which may be due to non-measurable fluctuations in volumetric flow rate, non-achievement of instant injection of tracer in case of pulse input, and slight variations in the sampling period. Further, with increasing flow rate, concentration, exit age, and cumulative fractional curves shifted upward, and this behavior matches with the actual case. AU - Khatoon, Bushra AU - Kamil, Shoaib AU - Babu, Hitesh AU - Siraj Alam, M. ID - 12172 IS - Part 1 JF - Materials Today: Proceedings KW - General Medicine SN - 2214-7853 TI - Experimental analysis of Cascade CSTRs with step and pulse inputs VL - 78 ER - TY - JOUR AB - Flows through pipes and channels are, in practice, almost always turbulent, and the multiscale eddying motion is responsible for a major part of the encountered friction losses and pumping costs1. Conversely, for pulsatile flows, in particular for aortic blood flow, turbulence levels remain low despite relatively large peak velocities. For aortic blood flow, high turbulence levels are intolerable as they would damage the shear-sensitive endothelial cell layer2,3,4,5. Here we show that turbulence in ordinary pipe flow is diminished if the flow is driven in a pulsatile mode that incorporates all the key features of the cardiac waveform. At Reynolds numbers comparable to those of aortic blood flow, turbulence is largely inhibited, whereas at much higher speeds, the turbulent drag is reduced by more than 25%. This specific operation mode is more efficient when compared with steady driving, which is the present situation for virtually all fluid transport processes ranging from heating circuits to water, gas and oil pipelines. AU - Scarselli, Davide AU - Lopez Alonso, Jose M AU - Varshney, Atul AU - Hof, Björn ID - 14341 IS - 7977 JF - Nature SN - 0028-0836 TI - Turbulence suppression by cardiac-cycle-inspired driving of pipe flow VL - 621 ER - TY - THES AB - Most motions of many-body systems at any scale in nature with sufficient degrees of freedom tend to be chaotic; reaching from the orbital motion of planets, the air currents in our atmosphere, down to the water flowing through our pipelines or the movement of a population of bacteria. To the observer it is therefore intriguing when a moving collective exhibits order. Collective motion of flocks of birds, schools of fish or swarms of self-propelled particles or robots have been studied extensively over the past decades but the mechanisms involved in the transition from chaos to order remain unclear. Here, the interactions, that in most systems give rise to chaos, sustain order. In this thesis we investigate mechanisms that preserve, destabilize or lead to the ordered state. We show that endothelial cells migrating in circular confinements transition to a collective rotating state and concomitantly synchronize the frequencies of nucleating actin waves within individual cells. Consequently, the frequency dependent cell migration speed uniformizes across the population. Complementary to the WAVE dependent nucleation of traveling actin waves, we show that in leukocytes the actin polymerization depending on WASp generates pushing forces locally at stationary patches. Next, in pipe flows, we study methods to disrupt the self–sustaining cycle of turbulence and therefore relaminarize the flow. While we find in pulsating flow conditions that turbulence emerges through a helical instability during the decelerating phase. Finally, we show quantitatively in brain slices of mice that wild-type control neurons can compensate the migratory deficits of a genetically modified neuronal sub–population in the developing cortex. AU - Riedl, Michael ID - 12726 SN - 2663-337X TI - Synchronization in collectively moving active matter ER - TY - JOUR AB - Viscous flows through pipes and channels are steady and ordered until, with increasing velocity, the laminar motion catastrophically breaks down and gives way to turbulence. How this apparently discontinuous change from low- to high-dimensional motion can be rationalized within the framework of the Navier-Stokes equations is not well understood. Exploiting geometrical properties of transitional channel flow we trace turbulence to far lower Reynolds numbers (Re) than previously possible and identify the complete path that reversibly links fully turbulent motion to an invariant solution. This precursor of turbulence destabilizes rapidly with Re, and the accompanying explosive increase in attractor dimension effectively marks the transition between deterministic and de facto stochastic dynamics. AU - Paranjape, Chaitanya S AU - Yalniz, Gökhan AU - Duguet, Yohann AU - Budanur, Nazmi B AU - Hof, Björn ID - 13274 IS - 3 JF - Physical Review Letters KW - General Physics and Astronomy SN - 0031-9007 TI - Direct path from turbulence to time-periodic solutions VL - 131 ER - TY - JOUR AB - Whether one considers swarming insects, flocking birds, or bacterial colonies, collective motion arises from the coordination of individuals and entails the adjustment of their respective velocities. In particular, in close confinements, such as those encountered by dense cell populations during development or regeneration, collective migration can only arise coordinately. Yet, how individuals unify their velocities is often not understood. Focusing on a finite number of cells in circular confinements, we identify waves of polymerizing actin that function as a pacemaker governing the speed of individual cells. We show that the onset of collective motion coincides with the synchronization of the wave nucleation frequencies across the population. Employing a simpler and more readily accessible mechanical model system of active spheres, we identify the synchronization of the individuals’ internal oscillators as one of the essential requirements to reach the corresponding collective state. The mechanical ‘toy’ experiment illustrates that the global synchronous state is achieved by nearest neighbor coupling. We suggest by analogy that local coupling and the synchronization of actin waves are essential for the emergent, self-organized motion of cell collectives. AU - Riedl, Michael AU - Mayer, Isabelle D AU - Merrin, Jack AU - Sixt, Michael K AU - Hof, Björn ID - 14361 JF - Nature Communications TI - Synchronization in collectively moving inanimate and living active matter VL - 14 ER - TY - JOUR AB - The large-scale laminar/turbulent spiral patterns that appear in the linearly unstable regime of counter-rotating Taylor–Couette flow are investigated from a statistical perspective by means of direct numerical simulation. Unlike the vast majority of previous numerical studies, we analyse the flow in periodic parallelogram-annular domains, following a coordinate change that aligns one of the parallelogram sides with the spiral pattern. The domain size, shape and spatial resolution have been varied and the results compared with those in a sufficiently large computational orthogonal domain with natural axial and azimuthal periodicity. We find that a minimal parallelogram of the right tilt significantly reduces the computational cost without notably compromising the statistical properties of the supercritical turbulent spiral. Its mean structure, obtained from extremely long time integrations in a co-rotating reference frame using the method of slices, bears remarkable similarity with the turbulent stripes observed in plane Couette flow, the centrifugal instability playing only a secondary role. AU - Wang, B. AU - Mellibovsky, F. AU - Ayats López, Roger AU - Deguchi, K. AU - Meseguer, A. ID - 14754 IS - 2246 JF - Philosophical Transactions of the Royal Society A KW - General Physics and Astronomy KW - General Engineering KW - General Mathematics SN - 1364-503X TI - Mean structure of the supercritical turbulent spiral in Taylor–Couette flow VL - 381 ER - TY - JOUR AB - The first long-lived turbulent structures observable in planar shear flows take the form of localized stripes, inclined with respect to the mean flow direction. The dynamics of these stripes is central to transition, and recent studies proposed an analogy to directed percolation where the stripes’ proliferation is ultimately responsible for the turbulence becoming sustained. In the present study we focus on the internal stripe dynamics as well as on the eventual stripe expansion, and we compare the underlying mechanisms in pressure- and shear-driven planar flows, respectively, plane-Poiseuille and plane-Couette flow. Despite the similarities of the overall laminar–turbulence patterns, the stripe proliferation processes in the two cases are fundamentally different. Starting from the growth and sustenance of individual stripes, we find that in plane-Couette flow new streaks are created stochastically throughout the stripe whereas in plane-Poiseuille flow streak creation is deterministic and occurs locally at the downstream tip. Because of the up/downstream symmetry, Couette stripes, in contrast to Poiseuille stripes, have two weak and two strong laminar turbulent interfaces. These differences in symmetry as well as in internal growth give rise to two fundamentally different stripe splitting mechanisms. In plane-Poiseuille flow splitting is connected to the elongational growth of the original stripe, and it results from a break-off/shedding of the stripe's tail. In plane-Couette flow splitting follows from a broadening of the original stripe and a division along the stripe into two slimmer stripes. AU - Marensi, Elena AU - Yalniz, Gökhan AU - Hof, Björn ID - 14466 JF - Journal of Fluid Mechanics KW - turbulence KW - transition to turbulence KW - patterns SN - 0022-1120 TI - Dynamics and proliferation of turbulent stripes in plane-Poiseuille and plane-Couette flows VL - 974 ER - TY - THES AU - Hennessey-Wesen, Mike ID - 14641 KW - microfluidics KW - miceobiology KW - mutations KW - quorum sensing SN - 2663 - 337X TI - Adaptive mutation in E. coli modulated by luxS ER - TY - JOUR AB - Standard epidemic models exhibit one continuous, second order phase transition to macroscopic outbreaks. However, interventions to control outbreaks may fundamentally alter epidemic dynamics. Here we reveal how such interventions modify the type of phase transition. In particular, we uncover three distinct types of explosive phase transitions for epidemic dynamics with capacity-limited interventions. Depending on the capacity limit, interventions may (i) leave the standard second order phase transition unchanged but exponentially suppress the probability of large outbreaks, (ii) induce a first-order discontinuous transition to macroscopic outbreaks, or (iii) cause a secondary explosive yet continuous third-order transition. These insights highlight inherent limitations in predicting and containing epidemic outbreaks. More generally our study offers a cornerstone example of a third-order explosive phase transition in complex systems. AU - Börner, Georg AU - Schröder, Malte AU - Scarselli, Davide AU - Budanur, Nazmi B AU - Hof, Björn AU - Timme, Marc ID - 12134 IS - 4 JF - Journal of Physics: Complexity KW - Artificial Intelligence KW - Computer Networks and Communications KW - Computer Science Applications KW - Information Systems SN - 2632-072X TI - Explosive transitions in epidemic dynamics VL - 3 ER - TY - JOUR AB - Directed percolation (DP) has recently emerged as a possible solution to the century old puzzle surrounding the transition to turbulence. Multiple model studies reported DP exponents, however, experimental evidence is limited since the largest possible observation times are orders of magnitude shorter than the flows’ characteristic timescales. An exception is cylindrical Couette flow where the limit is not temporal, but rather the realizable system size. We present experiments in a Couette setup of unprecedented azimuthal and axial aspect ratios. Approaching the critical point to within less than 0.1% we determine five critical exponents, all of which are in excellent agreement with the 2+1D DP universality class. The complex dynamics encountered at the onset of turbulence can hence be fully rationalized within the framework of statistical mechanics. AU - Klotz, Lukasz AU - Lemoult, Grégoire M AU - Avila, Kerstin AU - Hof, Björn ID - 10654 IS - 1 JF - Physical Review Letters SN - 0031-9007 TI - Phase transition to turbulence in spatially extended shear flows VL - 128 ER - TY - JOUR AB - In Fall 2020, several European countries reported rapid increases in COVID-19 cases along with growing estimates of the effective reproduction rates. Such an acceleration in epidemic spread is usually attributed to time-dependent effects, e.g. human travel, seasonal behavioral changes, mutations of the pathogen etc. In this case however the acceleration occurred when counter measures such as testing and contact tracing exceeded their capacity limit. Considering Austria as an example, here we show that this dynamics can be captured by a time-independent, i.e. autonomous, compartmental model that incorporates these capacity limits. In this model, the epidemic acceleration coincides with the exhaustion of mitigation efforts, resulting in an increasing fraction of undetected cases that drive the effective reproduction rate progressively higher. We demonstrate that standard models which does not include this effect necessarily result in a systematic underestimation of the effective reproduction rate. AU - Budanur, Nazmi B AU - Hof, Björn ID - 11704 IS - 7 JF - PLoS ONE TI - An autonomous compartmental model for accelerating epidemics VL - 17 ER - TY - GEN AB - Codes and data for reproducing the results of N. B. Budanur and B. Hof "An autonomous compartmental model for accelerating epidemics" AU - Budanur, Nazmi B ID - 11711 TI - burakbudanur/autoacc-public ER - TY - CHAP AB - Streaky structures in the boundary layers are often generated by surface roughness elements and/or free-stream turbulence, and are known to have significant effects on boundary-layer instability. In this paper, we investigate the impact of two forms of streaks on the instability of supersonic boundary layers. The first concerns the streaks generated by an array of spanwise periodic and streamwise elongated surface roughness elements, and our interest is how these streaks influence the lower-branch viscous first modes, whose characteristic wavelength and frequency are on the classical triple-deck scales. By adapting the triple-deck theory in the incompressible regime to the supersonic one, we first derived a simplified system which allows for efficient calculation of the streaks. The asymptotic analysis simplifies a bi-global eigenvalue problem to a one-dimensional problem in the spanwise direction, showing that the instability is controlled at leading order solely by the spanwise-dependent wall shear. In the fundamental configuration, the streaks stabilize first modes at low frequencies but destabilize the high-frequency ones. In the subharmonic configuration, the streaks generally destabilize the first mode across the entire frequency band. Importantly, the spanwise even modes are of radiating nature, i.e. they emit acoustic waves spontaneously to the far field. Streaks of the second form are generated by low-frequency vortical disturbances representing free-stream turbulence. They alter the flow in the entire layer and their effects on instability are investigated by solving the inviscid bi-global eigenvalue problem. Different from the incompressible case, a multitude of compressible instability modes exists, of which the dominant mode is an inviscid instability associated with the spanwise shear. In addition, there exists a separate branch of instability modes that have smaller growth rates but are spontaneously radiating. AU - Liu, Jianxin AU - Marensi, Elena AU - Wu, Xuesong ED - Sherwin, Spencer ED - Schmid, Peter ED - Wu, Xuesong ID - 10820 SN - 1875-3507 T2 - IUTAM Laminar-Turbulent Transition TI - Effects of streaky structures on the instability of supersonic boundary layers VL - 38 ER - TY - JOUR AB - We investigate the local self-sustained process underlying spiral turbulence in counter-rotating Taylor–Couette flow using a periodic annular domain, shaped as a parallelogram, two of whose sides are aligned with the cylindrical helix described by the spiral pattern. The primary focus of the study is placed on the emergence of drifting–rotating waves (DRW) that capture, in a relatively small domain, the main features of coherent structures typically observed in developed turbulence. The transitional dynamics of the subcritical region, far below the first instability of the laminar circular Couette flow, is determined by the upper and lower branches of DRW solutions originated at saddle-node bifurcations. The mechanism whereby these solutions self-sustain, and the chaotic dynamics they induce, are conspicuously reminiscent of other subcritical shear flows. Remarkably, the flow properties of DRW persist even as the Reynolds number is increased beyond the linear stability threshold of the base flow. Simulations in a narrow parallelogram domain stretched in the azimuthal direction to revolve around the apparatus a full turn confirm that self-sustained vortices eventually concentrate into a localised pattern. The resulting statistical steady state satisfactorily reproduces qualitatively, and to a certain degree also quantitatively, the topology and properties of spiral turbulence as calculated in a large periodic domain of sufficient aspect ratio that is representative of the real system. AU - Wang, B. AU - Ayats López, Roger AU - Deguchi, K. AU - Mellibovsky, F. AU - Meseguer, A. ID - 12137 JF - Journal of Fluid Mechanics KW - Mechanical Engineering KW - Mechanics of Materials KW - Condensed Matter Physics KW - Applied Mathematics SN - 0022-1120 TI - Self-sustainment of coherent structures in counter-rotating Taylor–Couette flow VL - 951 ER - TY - JOUR AB - Theoretical foundations of chaos have been predominantly laid out for finite-dimensional dynamical systems, such as the three-body problem in classical mechanics and the Lorenz model in dissipative systems. In contrast, many real-world chaotic phenomena, e.g., weather, arise in systems with many (formally infinite) degrees of freedom, which limits direct quantitative analysis of such systems using chaos theory. In the present work, we demonstrate that the hydrodynamic pilot-wave systems offer a bridge between low- and high-dimensional chaotic phenomena by allowing for a systematic study of how the former connects to the latter. Specifically, we present experimental results, which show the formation of low-dimensional chaotic attractors upon destabilization of regular dynamics and a final transition to high-dimensional chaos via the merging of distinct chaotic regions through a crisis bifurcation. Moreover, we show that the post-crisis dynamics of the system can be rationalized as consecutive scatterings from the nonattracting chaotic sets with lifetimes following exponential distributions. AU - Choueiri, George H AU - Suri, Balachandra AU - Merrin, Jack AU - Serbyn, Maksym AU - Hof, Björn AU - Budanur, Nazmi B ID - 12259 IS - 9 JF - Chaos: An Interdisciplinary Journal of Nonlinear Science KW - Applied Mathematics KW - General Physics and Astronomy KW - Mathematical Physics KW - Statistical and Nonlinear Physics SN - 1054-1500 TI - Crises and chaotic scattering in hydrodynamic pilot-wave experiments VL - 32 ER - TY - JOUR AB - We report frictional drag reduction and a complete flow relaminarization of elastic turbulence (ET) at vanishing inertia in a viscoelastic channel flow past an obstacle. We show that the intensity of the observed elastic waves and wall-normal vorticity correlate well with the measured drag above the onset of ET. Moreover, we find that the elastic wave frequency grows with the Weissenberg number, and at sufficiently high frequency it causes a decay of the elastic waves, resulting in ET attenuation and drag reduction. Thus, this allows us to substantiate a physical mechanism, involving the interaction of elastic waves with wall-normal vorticity fluctuations, leading to the drag reduction and relaminarization phenomena at low Reynolds number. AU - Kumar, M. Vijay AU - Varshney, Atul AU - Li, Dongyang AU - Steinberg, Victor ID - 12279 IS - 8 JF - Physical Review Fluids KW - Fluid Flow and Transfer Processes KW - Modeling and Simulation KW - Computational Mechanics SN - 2469-990X TI - Relaminarization of elastic turbulence VL - 7 ER -