Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session C11: Non-Linear Dynamics: Coherent Structures I |
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Chair: Roman Gregoriev, Georgia Institute of Technology Room: 3B |
Sunday, November 24, 2019 8:00AM - 8:13AM |
C11.00001: Homoclinic Orbits to Streamwise-Localized Solution in Pipe Flow Julius Rhoan Lustro, Genta Kawahara, Masaki Shimizu We do numerical study on transition to turbulence in pipe flow by investigating a streamwise-localized solution. We explore the trajectory along the unstable manifold of the lower branch of this time-periodic solution and found the presence of homoclinic orbits related to it. These homoclinic orbits are extracted by performing a bisection method. The presence of homoclinic orbits implies the existence of a Smale horseshoe which generates chaos and can be evidence to support a theoretical description of the onset of spatially localized transient turbulence -- i.e., turbulent puff -- observed in pipe flow experiments. [Preview Abstract] |
Sunday, November 24, 2019 8:13AM - 8:26AM |
C11.00002: Self-similar invariant solution in the near-wall region of a turbulent boundary layer at very high Reynolds numbers Tobias M. Schneider, Sajjad Azimi At sufficiently high Reynolds numbers, shear-flow turbulence close to a wall acquires universal properties. When length and velocity are rescaled by appropriate characteristic scales of the turbulent flow and thereby measured in inner units, the statistical properties of the flow become independent of the Reynolds number. We demonstrate the existence of a wall-attached exact invariant solution of the fully nonlinear 3D Navier-Stokes equations for a parallel boundary layer that captures the characteristic self-similar scaling of near-wall turbulent structures. The solution branch can be followed up to Re=500,000 corresponding to a friction Reynolds number in the millions. Combined theoretical and numerical evidence suggests that the solution is asymptotically self-similar and exactly scales in inner units for Reynolds numbers tending to infinity. Demonstrating the existence of invariant solutions that captures the self-similar scaling properties of turbulence in the near-wall region is a step towards extending the dynamical systems approach to turbulence from the transitional regime to fully developed boundary layers. [Preview Abstract] |
Sunday, November 24, 2019 8:26AM - 8:39AM |
C11.00003: Heteroclinic and Homoclinic Connections in a Kolmogorov-Like Flow Balachandra Suri, Ravi Kumar Pallantla, Logan Kageorge, Michael F. Schatz, Roman O. Grigoriev Recent studies suggest that unstable recurrent solutions of the Navier-Stokes equation provide new insights into dynamics of turbulent flows. In this study, we compute an extensive network of dynamical connections between such solutions in a weakly turbulent quasi-two-dimensional Kolmogorov flow that lies in the inversion-symmetric subspace. In particular, we find numerous isolated heteroclinic connections between different types of solutions -- equilibria, periodic, and quasi-periodic orbits -- as well as continua of connections forming higher-dimensional connecting manifolds. We also compute a homoclinic connection of a periodic orbit and provide strong evidence that the associated homoclinic tangle forms the chaotic repeller that underpins transient turbulence in the symmetric subspace. [Preview Abstract] |
Sunday, November 24, 2019 8:39AM - 8:52AM |
C11.00004: Unstable Periodic Orbits in Experimental Kolmogorov-Like Flow Logan Kageorge, Balachandra Suri, Roman Grigoriev, Michael Schatz The geometry of state space for a moderately turbulent flow is shaped by non-chaotic Navier-Stokes solutions known as Exact Coherent Structures (ECS). It has been shown in numerical studies of pipe flow that unstable periodic orbits, one such ECS, guide the evolution of nearby trajectories and form the backbone of the chaotic attractor. However, until now little experimental work has been done to show if periodic orbits are frequently visited in fluid systems and are therefore relevant to the dynamics of the system. We report on numerical work to identify periodic orbits and describe their dynamical relevance in experiments of weakly turbulent quasi-two-dimensional Kolmogorov-like flows. [Preview Abstract] |
Sunday, November 24, 2019 8:52AM - 9:05AM |
C11.00005: Experimental evidence of exact coherent structures in small-aspect-ratio Taylor-Couette flow Christopher J. Crowley, Michael C. Krygier, Wesley Toler, Roman O. Grigoriev, Michael F. Schatz Recent work suggests that the dynamics of turbulent wall-bounded flows are guided by unstable solutions to the Navier-Stokes 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 in 3D fluid flows computed ECS in streamwise-periodic domains that differed from the inflow-outflow 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 3D turbulent flow by directly comparing experimental measurements with numerical simulations at the same parameter values and boundary conditions in a small-aspect-ratio ($\Gamma=1$) turbulent Taylor-Couette flow with radius ratio $\eta = 0.71$. To detect an ECS, time-resolved 3D-3C velocity measurements were performed in the entire flow domain and compared to exact solutions of the Navier-Stokes equation obtained via fully-resolved direct numerical simulation. [Preview Abstract] |
Sunday, November 24, 2019 9:05AM - 9:18AM |
C11.00006: The mechanism of long turbulent lifetimes in a low-dimensional model of plane Couette flow James Hitchen, Alexander Morozov Recently, our understanding of the transition to turbulence has significantly changed due to the discovery of exact solutions of the Navier-Stokes equations and the introduction of the self-sustaining process in parallel shear flows. This theory has been very successful in describing the main features of weakly turbulent states, including the metastable nature of turbulence close to the transition and the super-exponential dependence of its lifetime on the Reynolds number. The main strength of this approach is that it allows for a semi-analytical description of the turbulent dynamics in the form of a rather low-dimensional model. Here we systematically develop a novel low-dimensional model that allows us to investigate the origin of the very long turbulent life-times close to the transition. We find that there exists a particular periodic orbit that acts as a porous reflecting barrier between the laminar and turbulent states, and that serves to greatly increase the time before relaminarisation. [Preview Abstract] |
Sunday, November 24, 2019 9:18AM - 9:31AM |
C11.00007: Heteroclinic Connections as Predictors of Extreme Events in Weakly Turbulent Flow Joshua Pughe Sanford, Roman O. Grigoriev Formally, extreme events occur in dynamical systems when an observable varies from its mean by many standard deviations. In practice, this describes events such as earthquakes, rogue waves, seizures, and heart attacks. Due to the catastrophic nature of these events on both an environmental and personal scale, an understanding of how these events occur is crucial. We investigate a two-dimensional Kolmogorov flow, where extreme events correspond to short-lived spikes in global dissipation. Using direct-adjoint iterations, we found a number of heteroclinic connections between unstable recurrent solutions characterized by very different rates in dissipation. We also found that extreme events correspond to the turbulent trajectories shadowing some of these connections in state space. These results suggest that heteroclinic connections may be used to understand and predict extreme events in this and other systems. [Preview Abstract] |
Sunday, November 24, 2019 9:31AM - 9:44AM |
C11.00008: Finding unstable periodic orbits with polynomial optimization, with application to a nine-mode model of shear flow. Mayur Lakshmi, Giovanni Fantuzzi, Jesus Fernandez-Caballero, Yongyun Hwang, Sergei Chernyshenko It was recently suggested (Tobasco et al. Phys. Lett. A, \textbf{382}, 382--386, (2018)) that trajectories of ODE systems which optimize the infinite-time average of an observable can be localized using sublevel sets of a function that arise when bounding such averages using so-called auxiliary functions. This talk will demonstrate that this idea allows for the computation of extremal unstable periodic orbits (UPOs) for polynomial ODE systems. We first show that polynomial optimization is guaranteed to produce near-optimal auxiliary functions, which are required to localize the extremal UPO accurately. We then show that points inside the relevant sublevel sets can be computed efficiently through direct nonlinear optimization. Such points provide good initial conditions for UPO computations. We illustrate the potential of this new technique of finding UPOs by presenting the results of applying it to a nine-dimensional model of a sinusoidally forced shear flow. [Preview Abstract] |
Sunday, November 24, 2019 9:44AM - 9:57AM |
C11.00009: The recurrence of flow structures in a low Re wake downstream of two cylinders. Huixuan Wu, Meihua Zhang, Zhongquan Zheng The recurrence network method is used to study the evolution of coherent structures in the wake downstream of two cylinders. The upstream cylinder is fixed and the downstream cylinder oscillates in the transverse direction at a fixed frequency. The vortices shed from the upstream cylinder interact with those from the other cylinder, generating a complicated vorticity distribution. Proper orthogonal decomposition is used to extract coherent structures from the vorticity field, but the modes, which are spatial distributions of vorticity, provide limited information about the temporal evolution of the system. In order to analyze the evolution, the time dependent modal coefficients are used to construct a high dimensional phase space. The flow evolution is represented by a trajectory in this space. At the Reynolds number studied in this work, the system keeps visiting the neighborhood of a previous state, though it never exactly repeats itself. This kind of visit can be regarded as recurrence within a certain tolerance. The network manifests a few recurrence patterns, which corresponds to the ways of evolution of the flow field. The result shows that the recurrence network is an effective tool to analyze the temporal evolution of coherent structures. [Preview Abstract] |
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