Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session D01: Nonlinear Dynamics: Coherent Structures I |
Hide Abstracts |
Chair: Rich Kerswell, University of Cambridge Room: Georgia World Congress Center B201 |
Sunday, November 18, 2018 2:30PM - 2:43PM |
D01.00001: Exact Coherent Structures in a Quasi-Two-Dimensional Kolmogorov-like Flow Balachandra Suri, Jeffrey R Tithof, Logan Kageorge, Ravi Kumar Pallantla, Roman O Grigoriev, Michael F Schatz Recent studies suggest that unstable, non-chaotic solutions of the Navier-Stokes equation may provide deep insights into fluid turbulence. In this talk, we present a combined experimental and numerical study of a weakly turbulent quasi-two-dimensional flow in an electromagnetically driven shallow fluid layer. |
Sunday, November 18, 2018 2:43PM - 2:56PM |
D01.00002: Dynamical connections between Exact Coherent Structures in Kolmogorov flow Logan Kageorge, Balachandra Suri, Ravi Kumar Pallantla, Roman O Grigoriev, Michael F Schatz The geometry of state space for a turbulent flow can be shaped by non-chaotic Navier-Stokes solutions known as Exact Coherent Structures (ECS), which influence the evolution of flows in their neighborhood. We report on experimental and numerical work to identify and characterize heteroclinic connections between ECS that may serve to guide turbulent flows from the neighborhood of one ECS to that of another. Using symmetry considerations, we have discovered two such connections, calculated in a numerical model of a Kolmogorov flow. We describe efforts to test the dynamical relevance of these heteroclinic orbits in experiments on weakly turbulent quasi-two-dimensional Kolmogorov flows. |
Sunday, November 18, 2018 2:56PM - 3:09PM |
D01.00003: Multiresolution Optimized Dynamic Mode Decomposition Nasser Heydari, Nathan Kutz, Panayiotis Diplas The performance of exact-DMD, optimized-DMD, and Multiresolution optimized-DMD are examined for an intricate flow around a vertical retaining wall structure embedded in a gravel bed. The experimental configuration is of paramount interests for the practitioners dealing with sediment erosion around the base of instream structures. The measurements were obtained employing a stereo particle image velocimetry (SPIV) in a plane perpendicular to the approach flow direction at the leading edge of the protrusion. The results indicate that optimized-DMD outperforms exact-DMD as it pulls out the stable modes. However, the flow under consideration is too complex, consist of multi-temporal and spatial scales, that it requires a large number of modes to approximate the coherent structures present in the flow. Thus, multiresolution optimized-DMD capable of separating slow and fast moving modes in a recursive manner is employed. Two criteria are considered for the selection of modes at each level: 1) a frequency cut-off, and 2) energy content. This is a robust approach to separate complex systems into a hierarchy of important multiresolution time-scale components. |
Sunday, November 18, 2018 3:09PM - 3:22PM |
D01.00004: Uniform shear flow: the state space of near-wall turbulence as Re_{τ }tends to ∞ Patrick Doohan, Ashley P Willis, Yongyun Hwang There is a growing body of evidence that self-similar coherent structures in the form of Townsend's attached eddies exist. Each of these structures bears a self-sustaining process remarkably similar to that of the near-wall region. To model this universal feature of wall-bounded turbulence, we have designed a shear flow model of near-wall turbulence applicable to various parallel shear flows as Re_{τ} tends to ∞. As a first step, we consider the minimal unit of near-wall turbulence: the governing equations are rescaled in inner units, while a constant shear stress is imposed as the top boundary condition of the domain located at y^{+}≈90. The model is validated against Couette flow, the near-wall region of which is independent of Reynolds number, and there is excellent agreement between velocity statistics & spectra for y^{+}<60. Thirteen relative equilibrium solutions are presented, the first discovered for this flow configuration. Through continuation in the spanwise width L_{z}^{+}, the bifurcation behaviour of the equilibria over domain size is examined. The physical properties of the equilibria are also explored through state space projection. Finally, the asymptotic behaviour of the equilibria is studied and three lower-branch solutions are found to scale consistently with VWI theory. |
Sunday, November 18, 2018 3:22PM - 3:35PM |
D01.00005: Density homogenization of a stratified exact coherent structure at high Prandtl number Jake Langham, Tom Eaves, Rich Kerswell We study a family of stably stratified unstable equilibria in plane Couette flows as the Prandtl number Pr — the ratio of viscosity to thermal diffusivity — varies. In both the small and large Pr limits, these states persist at high global Richardson numbers (>> 1/4) without being disrupted by stratification. For large Pr, the channel interior becomes well-mixed, forcing strongly stably stratified boundary layers to form near the walls. This layering makes the equilibria indifferent to the imposed density difference between the walls in the limit. As far as we are aware, this is the first example of layering in an exact numerical solution to the stratified Navier-Stokes equations. |
Sunday, November 18, 2018 3:35PM - 3:48PM |
D01.00006: Searching for periodic orbits in turbulent flows using machine learning Jacob Page, Rich Kerswell, Michael Brenner Our understanding of fluid turbulence has improved through the discovery of large numbers of unstable solutions to the Navier-Stokes equations. A turbulent trajectory bounces between these exact coherent states (ECS), being drawn in and then flung out along their stable and unstable manifolds. This low-dimensional view of turbulence proves difficult to extend beyond moderate Reynolds numbers due to inherent difficulties in identifying the ECS which are visited only fleetingly, while standard dimensionality reduction techniques like POD are unrelated to and mask ECS. Motivated by these observations, we explore whether deep neural networks can be used to identify low-order projections of turbulence that respect the existence of ECS by training a convolutional autoencoder to reconstruct snapshots from turbulent 2D Kolmogorov flows. The encoded representation reduces the number of degrees of freedom by several of orders of magnitude. We then compute the encoded representations of a large number of ECS to see how well separated these solutions are in the encoded space. Finally, we discuss how the approach can be used to extract ECS at high Reynolds number. |
Sunday, November 18, 2018 3:48PM - 4:01PM |
D01.00007: The role of exact coherent structures in turbulent small-aspect-ratio Taylor-Couette flow Michael C Krygier, Roman O Grigoriev The interpretation of fluid turbulence as a deterministic walk between neighborhoods of unstable nonchaotic solutions of the Navier-Stokes equation (known as exact coherent structures, ECS) has offered a new perspective on the physical mechanisms that sustain the turbulent dynamics and control the transition from laminar flow. In particular, we have demonstrated that ECS in weakly turbulent Taylor-Couette flow can be found using a combination of recurrence analysis and parameter continuation. The relative periodic orbits and relative equilibria that we computed were shown to play a dynamically important role. In particular, their neighborhoods are visited closely and frequently by the turbulent flow. Furthermore, saddle-node bifurcations at which some of these solutions (dis)appear correspond quite precisely to qualitative changes in turbulent dynamics and/or relaminarization of the flow. |
Sunday, November 18, 2018 4:01PM - 4:14PM |
D01.00008: Experimental search for exact coherent structures in turbulent small-aspect-ratio Taylor-Couette flow Christopher J Crowley, Michael C Weaver, Michael C Krygier, Roman O Grigoriev, Michael F Schatz Recent work suggests that the dynamics of turbulent shear driven flows are guided by special unstable solutions to the Navier-Stokes equations that have nontrivial spatial structure and temporally simple dynamics. These solutions, known as exact coherent structures (ECS), play a key role in a fundamentally deterministic description of turbulence. Here we report preliminary results from a small-aspect-ratio (Γ = 1) Taylor-Couette system at a radius ratio of η = 0.7 where time resolved 3D-3C velocity measurements are performed in the entire flow domain. In particular, we compare, at the same parameter values, experimental measurements of turbulent flow with ECS computed in Direct Numerical Simulation. |
Sunday, November 18, 2018 4:14PM - 4:27PM |
D01.00009: Dynamic feedback control of edge states in plane Poiseuille flow Bruno Eckhardt, Florian Knierim, Moritz Linkmann The transition to turbulence in many wall-bounded parallel shear flows, such as pipe or plane Poiseuille flow, is connected to the presence of a lower-dimensional manifold in state space, the edge of chaos, which distinguishes between initial conditions resulting in laminar or turbulent flow. States on the edge manifold have thus at least one unstable direction, and the dynamics will not remain confined to it. However, feedback stabilisation method can be used to remove the effect of the unstable direction, as demonstrated for pipe flow by Willis et al JFM 2017. Here, we focus on similar strategies in plane Poiseuille flow. We investigate the effect of a dynamic pressure-based feedback control on the stable and unstable directions in order to stabilise states on the edge. |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2023 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
1 Research Road, Ridge, NY 11961-2701
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700