Bulletin of the American Physical Society
73rd Annual Meeting of the APS Division of Fluid Dynamics
Sunday–Tuesday, November 22–24, 2020; Virtual, CT (Chicago time)
Session Y03: Nonlinear Dynamics: Transition to Turbulence (11:30am  12:15pm CST)Interactive On Demand

Hide Abstracts 

Y03.00001: Anisotropic Decay of Turbulence in Plane CouettePoiseuille Flow Tao Liu, Benoit Semin, Lukasz Klotz, Ramiro GodoyDiana, Jose Eduardo Wesfreid, Tom Mullin We report the results of an experimental investigation into the decay of turbulence in CouettePoiseuille flow using socalled 'quench' experiments where the flow laminarises after a sudden reduction in Reynolds number. We measured the velocity field in the $xz$ plane, where $x$ is the streamwise and $z$ the spanwise directions respectively. We show that the decay of turbulence is anisotropic: the spanwise velocity $u_z$, corresponding to streamwise vortices (or rolls), decays faster than the streamwise velocity $u_x$, corresponding to elongated regions of higher or lower velocity named streaks. We define turbulent fractions $F_x$ and $F_z$ from the streamwise $x$ and spanwise $z$ velocity components, respectively, and examine their decay as a function of the Reynolds number. The decay of $F_z$ is linear and always faster than the one of $F_x$, while the decay of the spanwise energy $E_z$ fits an exponential. We characterized the decay rate $A_z$ of $E_z$ and the decay slope $a_z$ of $F_z$ as a function of $Re$. We found that the obtained values are independent of the noise levels. Both the decay rates $A_z$ and the decay slopes $a_z$ scale in the form $\propto(Re_*Re)$, with $Re_*$ close to $Re=670$ above which turbulence becomes selfsustained. [Preview Abstract] 

Y03.00002: A linear matrix inequality based approach for efficient approximation of permissible perturbation amplitude in wallbounded shear flows at transitional Reynolds numbers Chang Liu, Dennice Gayme The parameters governing transition to turbulence in wallbounded shear flows have been widely studied, but a wide gap between analytically attained (provable) parametric bounds and experimental/simulation results remains. Here, we focus on one aspect of this problem, providing provable Reynolds number (Re) dependent bounds on the amplitude of perturbations a flow can sustain while maintaining the laminar state. Our analysis relies on a (Lure) partitioning of the dynamics into a feedback interconnection between the linear and nonlinear dynamics. We then derive constraints on the nonlinear term based on its known physical properties (energy conservation and bounded inputoutput energy). These constraints are used to formulate the computation of permissible perturbation amplitude as linear matrix inequality constrained optimization problem. Our analytically derived bounds are less conservative than those obtained through linear analysis or classical energy methods. The results are also consistent with those identified through exhaustive simulations for a range of low dimensional nonlinear shear flow models. However, they are achieved at much lower computational cost and provide a provable guarantee that a certain level of perturbation is permissible. [Preview Abstract] 

Y03.00003: From linear stability to selfsustaining solutions: Taylor vortex flow through the lens of resolvent analysis Benedikt Barthel, Xiaojue Zhu, Beverley McKeon Taylor vortices are known to arise due to a centrifugally driven, supercritical instability of the laminar base flow. However, as the Reynolds number increases past the critical value, the Taylor vortices are no longer driven by centrifugal mechanisms, but are instead driven by nonlinear interactions reminiscent of a selfsustaining process and thus persist well beyond the onset of turbulence (Sacco et al., JFM, 2019). Here we use the resolvent formulation of McKeon and Sharma to model this transition from linear instability to nonlinear Taylor vortices. Near the critical Reynolds number, we show that the Reynolds stress is accurately modeled by the selfinteraction of a single eigenmode of the unstable base flow, highlighting the linear amplification mechanisms at play, and circumventing the reliance on an a priori known mean profile. We then efficiently and accurately model the fully nonlinear Taylor vortex flow by treating the nonlinearity not as an inherent part of the governing equations but rather as a triadic constraint which must be satisfied by the model solution. These results could allow for a systematic algorithm to bootstrap solutions up in Reynolds number starting from the bifurcation from the laminar state well into the nonlinear regime. [Preview Abstract] 

Y03.00004: Statistical transition to turbulence in plane channel flow S\'ebastien Gom\'e, Laurette Tuckerman, Dwight Barkley Transition to turbulence in shear flows is characterized by intermittent laminarturbulent patterns, which statistically proliferate or decay depending on the Reynolds number. The evolution of turbulent bands in plane channel flow is studied via direct numerical simulations in a narrow computational domain tilted with respect to the streamwise direction. Bands interact via their intervening quasilaminar gap, impacting their propagation velocities. Turbulence decay and spreading processes are in most cases exponentially distributed, which is the signature of a memoryless process. Statistically estimated time scales for band decay or splitting depend superexponentially on the Reynolds number and lead to the estimation of Reynolds number $Re_{\rm{cross}}\simeq 965$ above which splitting is more likely than decay. The associated time scales are over $10^6$ advection times. With such a low associated probability, the use of statistical mechanics methods such as a rare event algorithm is necessary to evaluate the mean decay or splitting time. Decay or splitting events are analyzed through the dynamics of largescale Fourier components of the velocity, which statistically approaches a mostprobable pathway. [Preview Abstract] 

Y03.00005: On the Htype transition to turbulence: Laboratory experiments and reducedorder modeling Shyuan Cheng, Leonardo Chamorro, Phillip Ansell A laboratory investigation was conducted to explore the sources of local, highamplitude velocity fluctuations produced at the late stage of boundary layer transition. The velocity fluctuations were induced with TollmienSchlichting (TS) waves into a laminar flatplate boundary layer under a zeropressure gradient. Proper orthogonal decomposition (POD) was used to extract the dominant modal contributions within this transitional flow. The first four POD modes exhibited spatial shapes consistent with canonical hairpin vortices; also, a peak frequency matching that of the fundamental TS wave is evidenced in the timedependent mode coefficients. Higherorder modes demonstrate a combination of sub and superharmonics of the TS wave frequency, these higher modes represent hairpin packets. A reducedorder model for the Reynolds shear stress (RSS) overshoot is proposed by considering conditional averaging. The model shows that the first four POD modes with {\$}$\backslash $approx{\$} 15$\backslash ${\%} of the energy captured {\$}$\backslash $approx{\$} 85$\backslash ${\%} of the peak RSS amplitude at the overshoot location, indicating that lower portion of largescale hairpin vortices is largely responsible for the overshoot mechanism. [Preview Abstract] 

Y03.00006: Rare eventtriggered transitions in aerodynamic bifurcation: a model from the transition to turbulence Ariane Gayout, Mickael Bourgoin, Nicolas Plihon Subcritical bifurcations in flows encompass a wide diversity of phenomena, spanning from the transition to turbulence to wake instability on 3D bluff bodies. When subject to a flow in a wind tunnel, a disk pendulum presents a subcritical bifurcation with the coexistence of two aerodynamic branches, one governed by drag and the other by lift. Between these branches, spontaneous transitions are observed experimentally. The waiting times ahead of the transitions are distributed following a doubleexponential as a function of the control parameter, covering four orders of magnitude in time, for both transitions, thus reminding of the transition to turbulence. Applying a model originally thought for the transition to turbulence, we show that the observed transitions are controlled by rare events occurring in the aerodynamic forces acting on the disk. We then link these events to vortex sheddinginduced fluctuations. By studying a simple yet complex in its behavior system, this work provides a direct application of transitiontoturbulence models that could be further extended to other outofequilibrium systems. [Preview Abstract] 

Y03.00007: The edge of chaos as a Lagrangian Coherent Structure Miguel Beneitez, Yohann Duguet, Philipp Schlatter, Dan S. Henningson The linear stability analysis of many shear flows e.g. plane Couette flow, indicates that no infinitesimal perturbations grow exponentially. However, it is known that for such flows transition to turbulence occurs for perturbations of a finite amplitude. The state space of such systems is structured around a dividing manifold called the edge, which separates trajectories attracted by the laminar state from those reaching the turbulent state. We apply here concepts and tools from Lagrangian data analysis to investigate this edge manifold. In this work the edge manifold is reinterpreted as a hyperbolic Lagrangian coherent structure, being the locally most repelling surface in state space. Two different diagnostics, finitetime Lyapunov exponents (FTLEs) and Lagrangian Descriptors, are used and compared with respect to their ability to identify the edge and to their scalability. Their properties are illustrated on several loworder models of subcritical transition of increasing dimension and complexity, as well on wellresolved simulations of the NavierStokes equations in the case of plane Couette flow. [Preview Abstract] 

Y03.00008: Experimental observation of Duffing dynamics in liquid sloshing Kerstin Avila, Bastian Baeuerlein The nonlinear resonances of sloshing liquids in ships (e.g. liquified natural gas) and of liquid fuel in rockets pose serious risks. Their dynamics resembles that Duffing of oscillators and it has been predicted with potential theory that sloshing in a rectangular container obeys the Duffing equation. However, potential theory does not include dissipation and even for modern sloshing models the description of dissipation remains a challenge, which prevents predictions of the nonlinear response maxima. \newline We show that lowamplitude sloshing in a horizontally oscillated rectangular tank obeys Duffing dynamics with linear damping. The motion of the liquid's centre of mass is used to characterize the amplitude and phaselag of the sloshing unambiguously and globally. As the driving amplitude increases deviations from Duffing dynamics are first seen in the phaselag, well before complex wave patterns emerge. We observe that at resonance the sloshing motion is in quadrature with the driving independently of the observed flow state. This confirms the theoretical $90^\circ$phaselag criterion and highlights the phaselag (so far rarely measured in experiments) as a key indicator of transitions in sloshing liquids. [Preview Abstract] 

Y03.00009: Modeling a turbulent flow using periodic orbits Nazmi Burak Budanur, G\"{o}khan Yalniz, Bj\"{o}rn Hof We show that turbulence in simulations of the sinusoidallydriven NavierStokes equations in three dimensions can be decomposed into a series of shadowing events wherein the dynamics can be transiently approximated by a periodic orbit. Based on its shadowing decomposition, we generate a lowdimensional model of the turbulent flow as a Markov chain with nodes corresponding to the periodic orbits. We show that the invariant measure of the Markov chain provides periodic orbit weights that capture the flow statistics. Our results suggest that the neighborhoods of periodic orbits yield an approximation to the natural measure of the turbulent flow. [Preview Abstract] 

Y03.00010: Interpreted machine learning in fluid dynamics: Explaining relaminarization events in wallbounded shear flows Martin Lellep, Jonathan Prexl, Moritz Linkmann, Bruno Eckhardt Machine Learning (ML) is becoming increasingly popular in dataintensive research, including fluid dynamics. Traditionally, powerful ML algorithms such as neural networks or ensemble methods sacrifice interpretability, rendering them suboptimal for tasks where understanding is essential. Here, we use the novel Shapley Additive Explanations (SHAP) algorithm, a gametheoretic approach that explains the ML model output, to ascertain the extent to which specific physical processes drive the prediction of relaminarization events in wallbounded parallel shear flows. We use a gradient boosted tree ensemble model for the prediction, reaching up to $90\%$ accuracy for a prediction horizon of $5$ Lyapunov times in the future. The flow is described by the established ninemodel model for wallbounded parallel shear flows near the onset of turbulence, that comes with a physical and dynamical interpretation in terms of streaks, vortices and linear instabilities. Apart from the laminar profile, the mode associated with the streamwise vortex, a characteristic feature of wallbounded parallel shear flows, is consistently playing a major role in the prediction. We thus demonstrate that explainable AI methods can provide useful and humaninterpretable insights for fluid dynamics. [Preview Abstract] 

Y03.00011: Symmetryreduced Dynamic Mode Decomposition of the nearwall turbulence in channel flow Elena Marensi, Gokhan Yalniz, Bjoern Hof, Nazmi Burak Budanur In the past ten years dynamic mode decomposition (DMD) has emerged as a powerful tool for the datadriven characterization of largescale systems, such as those that arise from complex fluid flow phenomena. DMD is based on singular value decomposition (SVD), which is known to struggle in systems with continuous symmetries, as the modal expansion is dominated by drifts and cannot, in general, provide information about the underlying physical mechanisms. Here, we tackle this problem for the case of plane Poiseuille flow by combining DMD with a preprocessing continuoussymmetry reduction that removes the translations both in the streamwise and spanwise directions. We consider a long turbulent trajectory in a minimal flow unit at a $Re = 2000$ and perform many DMD calculations over sliding windows of increasing durations. Tracking the DMD reconstruction error as a function of time, we uncover episodes of the turbulent evolution that can be well captured by a reduced linear expansion. In addition, we argue that identification of nearlycyclic processes via symmetryreduced DMD offers a datadriven method for discovering sustaining processes of nearwall turbulence. In both cases, symmetryreduction is found to be crucial to obtain meaningful representations of the system under stud [Preview Abstract] 
Not Participating 
Y03.00012: A better approach to assess mean flow stability in turbulence Rich Kerswell, Vilda Markeviciute There is a long history dating back to the 1950s of examining the stability of the turbulent mean profile in shear flows. Originally this was to explore the existence of a possible selection mechanism for the particular form of the mean flow and, latterly, has been used to help rationalise observed large scale structures seen in the turbulence. The stability `analysisâ€™ usually applied consists simply of studying the spectral properties of the OrrSommerfeld equation built around the turbulent mean. We will discuss how to extend this naive approach to the next level of sophistication. [Preview Abstract] 

Y03.00013: Buoyancysuppressed transition in vertical pipe flow Ashley Willis, Elena Marensi, Shuisheng He In many heating and cooling systems, the presence of turbulence in the flow is essential for effective heat transfer. The heat transfer itself, however, can `destabilise' the turbulence. In a vertical heated pipe, as heat transfer is increased, sheardriven turbulence can undergo a sudden laminarisation either to a simple parabolic flow or to a relatively quiescent convectiondriven state. \\ In this work, we consider the transition from sheardriven turbulence, initially in the dynamical systems context involving linear stability and invariant solutions. While certain nonlinear solutions are closely related to transition {\em to} turbulence, their relationship with transition {\em from} turbulence is more difficult to pin down. These solutions are clearly observed to be suppressed, but direct observations of the nature of roles of streaks in the heated flow is more revealing in determining the origin of turbulence suppression. [Preview Abstract] 

Y03.00014: Intermittent turbulence in a manybody system Guram Gogia, Wentao Yu, Justin Burton A wellknown example of intermittent dynamics is the generation of transient, turbulent ``puffs'' in fluid flow through a pipe with rough walls. Here we show how similar dynamics can emerge in a discrete, crystalline system of particles driven by noise. Polydispersity in particle masses leads to localized vibrational modes that effectuate a transition to a gaslike phase. A minimal model for the evolution of the system's mechanical energies exhibits quasicyclic oscillations, and a single, dimensionless number captures the essential features of the intermittent dynamics, analogous to the Reynolds number for pipe flow. [Preview Abstract] 

Y03.00015: Dynamics and statistics of weakly turbulent TaylorCouette flow in terms of Exact Coherent Structures Joshua Pughe Sanford, Roman Grigoriev Coherent structures are believed to play an important role in fluid turbulence. Transitional flows of Newtonian fluids provide an ideal setting for understanding and quantifying their impact on the dynamics and statistics of turbulence, where coherent structures correspond to unstable solutions of the NavierStokes equation. Previous studies have gone so far as to suggest that a single unstable solution can describe both the physical mechanism sustaining turbulence in wallbounded flows and its statistical properties, such as the mean flow profile. Our study of lowaspectratio ($\eta =$ 1/2, $\Gamma =$ 1) TaylorCouette flow at Reynolds number of order 1000 illustrates that  outside of minimal flow units  a rather large number of unstable solutions is needed to describe turbulence. We produce quantitative evidence that turbulent flow shadows numerous relative periodic orbits (RPOs)  the most common type of unstable solutions in this geometry. We also show that, while the mean flow profiles of turbulence and individual RPOs may be similar, there are significant quantitative differences in the associated observables, such as the torque exerted by the fluid on the cylinders. [Preview Abstract] 

Y03.00016: Identifying turbulent shadowing of 3D Exact Coherent Structures from measurements of 2D2C velocity measurements in smallaspectratio TaylorCouette flow Christopher J Crowley, Wesley Toler, Joshua PugheSanford, Kendra Sands, Roman O Grigoriev, Michael F Schatz Recent work suggests that the dynamics of turbulent wallbounded flows are guided by unstable solutions to the NavierStokes equation that have nontrivial spatial structure and temporally simple dynamics. These solutions, known as exact coherent structures (ECS), are presumed to play a key role in a fundamentally deterministic description of turbulence. Prior work on the role of ECS in 3D turbulence focused mainly on open flows in small computational domains with streamwiseperiodic boundary conditions that differ from the inflowoutflow boundary conditions of corresponding experimental tests, which relied on the use of Taylor's hypothesis to obtain laboratory measurements. Here we report evidence for ECS in a closed 3D turbulent flow by directly comparing experimental measurements with ECS computed numerically in a smallaspectratio ($\Gamma=1$) turbulent TaylorCouette flow with radius ratio $\eta=0.71$ which does not require the use of Taylor's hypothesis. We show that shadowing of ECS by turbulent flow can be detected by comparing timeresolved 2D2C velocity measurements in a 2D plane of the flow with the corresponding slice of an ECS. [Preview Abstract] 

Y03.00017: Experimental tests of dynamical and statistical relevance of exact coherent structures in turbulent smallaspectratio TaylorCouette flow Wesley Toler, Christopher J Crowley, Josh PugheSanford, Kendra Sands, Michael F Schatz, Roman O Grigoriev Recent work suggests that the dynamics of turbulent wallbounded flows are guided by unstable solutions to the NavierStokes equation that have nontrivial spatial structure and temporally simple dynamics. These solutions, known as exact coherent structures (ECS), are presumed to play a key role in a fundamentally deterministic description of turbulence, however experimental evidence for dynamical and statistical relevance of ECS is lacking. Here we examine an experimental TaylorCouette flow in a smallaspectratio geometry ($\Gamma =$1, radius ratio $\eta =$0.71). We show that the turbulent flow shadows a number of ECS of a particular type (relative periodic orbits) obtained numerically. We also show that statistical quantities, such as the mean flow profile, for the turbulent flow and various ECS are similar but not identical. [Preview Abstract] 

Y03.00018: Turbulent TwoPhase Flow of Kerosene and Water in a Vertical Pipe Carlos Plana, Marc Avila, Baofang Song Twophase flows in pipes exhibit a variety of flow patterns, which depend on the numerous dimensionless parameters that govern the system. A common approach to understand this rich dynamics was pioneered by D.D. Joseph and coauthors, who investigated the linear instabilities of a particular configuration called coreannular flow, in which a fluid of high viscosity (core) is surrounded by a fluid of lower viscosity (annulus). We compute the linear stability of coreannular flow of kerosene and water in a vertical pipe and find that it is highly unstable. By performing direct numerical simulations initialized with a slightly perturbed coreannular flow, we show that the system transitions to turbulence and relaxes to a stratified configuration in which water and kerosene flow alongside. Our work highlights the need for applying nonlineardynamics approaches to understand the physical mechanisms underlying the patterns observed in twophase pipe flows. [Preview Abstract] 

Y03.00019: Datadriven dynamics description of a transitional boundary layer Firoozeh Foroozan, Vanesa Guerrero, Andrea Ianiro, Stefano Discetti Cluster analysis is applied to a DNS dataset of a transitional boundary layer (BL) developing over a flat plate. The streamwisespanwise plane at a wall normal distance y=0.25 halfplate thickness L is sampled at several time instants and discretized into small subregionswith a size of 20Lx20L, which are the observations analysed in this work. Using kmedoids clustering algorithm, a partition of the observations is sought such that the medoids in each cluster represent the main local states. The clustering has been carried out on a twodimensional reducedorder feature space, constructed with the multidimensional scaling technique. The clustered feature space provides a partitioning which consists of five different regions, each one being represented by the cluster medoid. The observations are automatically classified as laminar, turbulent spots, amplification of disturbances, or fullydeveloped turbulence. The lagrangian evolution of the regions and the state transitions are described in terms of transition probability matrix and transition trajectory graph to determine the transition dynamics between the different states. [Preview Abstract] 

Y03.00020: Helical instability in pulsatile pipe flow. Atul Varshney, Duo Xu, Marc Avila, Bjorn Hof Fluid flow when subjected to periodic velocity modulations (e.g. cardiovascular flows) exhibit hydrodynamic instabilities and turbulence depending on frequency and amplitude of pulsation. Fluctuating shear stresses and disordered flow are responsible for cellular dysfunction in blood vessels, leading to the development of atherosclerotic lesions. We identify a nonlinear instability mechanism for pulsating pipe flow that gives rise to bursts of turbulence at low flow rates. Geometrical distortions of small, yet finite, amplitude are found to excite a state consisting of helical vortices during flow deceleration. The resulting flow pattern grows rapidly in magnitude, breaks down into turbulence, and eventually returns to laminar when the flow accelerates. This scenario causes shear stress fluctuations and flow reversal during each pulsation cycle. Further, we track the helical instability in a broad parameter space of Reynolds number and Womersley number, and towards nearly oscillatory flows, i.e. flows with small or no mean flow component. [Preview Abstract] 
Follow Us 
Engage
Become an APS Member 
My APS
Renew Membership 
Information for 
About APSThe American Physical Society (APS) is a nonprofit membership organization working to advance the knowledge of physics. 
© 2021 American Physical Society
 All rights reserved  Terms of Use
 Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 207403844
(301) 2093200
Editorial Office
1 Research Road, Ridge, NY 119612701
(631) 5914000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 200452001
(202) 6628700