Bulletin of the American Physical Society
74th Annual Meeting of the APS Division of Fluid Dynamics
Volume 66, Number 17
Sunday–Tuesday, November 21–23, 2021; Phoenix Convention Center, Phoenix, Arizona
Session T07: Nonlinear Dynamics: Coherent Structures |
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Chair: Mitul Luhar, Univeristy of South California Room: North 122 C |
Tuesday, November 23, 2021 12:40PM - 12:53PM |
T07.00001: Energy Transfer Mechanisms of Coherent Structures in Wakes via Mode Decomposition Daniel Foti Instabilities and compact vorticity are induced in turbulent wakes, which give rise to multi-scale coherent structures. The transfer of energy between turbulence scales plays a major role in coherent structure formation, evolution, and breakdown. The evolution of kinetic energy associated with the coherent fluctuations of these features can be quantified through a triple decomposition of the velocity fluctuations. A methodology is developed to quantify the transfer and transport of kinetic energy of individual coherent structure scales through mode decomposition, whereby the total coherent velocity is separated into a set of velocities classified on the scale of the mode. A highly interconnected system of equations of scale-specific coherent kinetic energy is used to describe inter-scale transport, transfer of energy, and coherent structure contributions to dissipation and from production. The coherent kinetic energy and its budget produced by the flow around a square cylinder at low and high Reynolds numbers obtained from direct numerical simulations are detailed. Dyadic and triadic interactions of modes that comprise terms in the coherent kinetic energy balance are explored, and interactions of turbulence scales are quantified. |
Tuesday, November 23, 2021 12:53PM - 1:06PM |
T07.00002: Time evolution of turbulent Taylor-Couette flow is robustly captured by Exact Coherent Structures Christopher J. Crowley, Joshua L. Pughe-Sanford, Wesley Toler, Roman O Grigoriev, Michael F Schatz Recent work has demonstrated that the time evolution of turbulent flows can be captured by simple, recurrent solutions of the Navier-Stokes equations called Exact Coherent Structures (ECSs). It is often assumed that an ECS quantitatively describes turbulence during an interval of time when turbulence is close (in state space) to the given ECS. In this talk, we present evidence suggesting that the dynamics of turbulence can be captured by ECSs with non-trivial temporal behavior even in cases where turbulence is not particularly close to an ECS. We have investigated numerous examples of turbulence co-evolving with (`shadowing') an ECS in a small-aspect-ratio Taylor-Couette flow. In this system, we have established a protocol for identifying intervals of time when turbulence shadows an ECS. We also discuss the difference in shadowing criteria for numerics and experiment. |
Tuesday, November 23, 2021 1:06PM - 1:19PM |
T07.00003: Generation of Hairpin Vortices and Computation of Associated Invariant Solutions in Plane Poiseuille Flow Aaron Carta, John F Gibson Hairpin vortices and their role in the dynamics of wall-bounded flows have |
Tuesday, November 23, 2021 1:19PM - 1:32PM |
T07.00004: Scale-Dependent Proper Orthogonal Decomposition to Study Scale Interaction in Turbulent Pipe Flow Data Akhileshwar Borra, Theresa Saxton-Fox Scale-dependent proper orthogonal decomposition (SD-POD) is a modal analysis technique used to extract multiple sets of orthogonal modes from a scalar or vector field based on the phase of a large-scale structure present in the flow field. To evaluate structure interaction in turbulent pipe flow, SD-POD was applied to particle image velocimetry data collected at the recirculating water pipe facility at Princeton University (Saxton-Fox et al., 2019). Two sets of orthogonal modes for small-scale structures were computed based on two phases of the large scale structure. Non-linear interaction between large- and small-scale structure in fluids causes the energy of the small-scale structures to be influenced by the large-scale structures (Mathis et al., 2009, Chung et al., 2010). In this talk, the SD-POD algorithm will be reviewed along with results from the turbulent pipe flow data. The pipe flow data results show the distance from the wall where small-scale modes are the strongest changes depending on the phase of the large-scale structure. |
Tuesday, November 23, 2021 1:32PM - 1:45PM |
T07.00005: Exploring Invariant Symmetry Subspaces of Channel Flow Pratik Aghor, John F Gibson Exact coherent structures (ECS) such as equilibria, traveling waves, periodic and relative periodic orbits, are known to be important in arranging the dynamics of a turbulent attractor. Several ECS have been found for canonical shear flows such as the plane Couette flow (PCF) and the pipe flow. However, less progress has been made for the case of plane Poiseuille flow (PPF). Many studies so far have used homotopy continuation, numerically continuing ECS from PCF conditions to PPF conditions. In the present study, some important invariant subspaces of PPF are explored. In particular, several new nonlinear traveling waves are identified in the <σy>, <σy, σz> and <σy, σzτx> subspaces, where σ represents reflection symmetry about the specified axis and τx denotes half-box shift in the streamwise x-direction, making σzτx a shift-reflect symmetry. Instead of homotopy continuation, guesses for the Newton-Krylov solver are taken directly from turbulent time-series, with appropriately imposed symmetries. Numerical continuation is used to continue the converged traveling wave solutions in Reynolds number. Subsequent bifurcations, including several symmetry-breaking bifurcations, are analyzed. |
Tuesday, November 23, 2021 1:45PM - 1:58PM |
T07.00006: Can We Connect a Dynamical Description and a Statistical Description of Turbulence? Joshua L. Pughe-Sanford, Michael C Krygier, Roman O Grigoriev For a class of chaotic systems, periodic orbit theory (POT) aims to connect a dynamical description with a statistical one by means of unstable solutions of the governing equations. It has been conjectured that a suitable extension of POT to systems with discrete and continuous symmetries can be used to describe the statistics of turbulent fluid flows. To test POT predictions, we investigate a weakly turbulent, small aspect-ratio Taylor–Couette flow driven by counter-rotating cylinders. This flow is realizable in experiment and has both discrete and continuous symmetries. Consequently, most of the unstable solutions found for this flow are relative periodic orbits (RPOs). We find that weighted sums over a collection of twelve RPOs accurately predict the turbulent average of kinetic energy, but not energy dissipation. Neither observables’ higher order moments are well predicted by the sums over RPOs. This discrepancy can be traced to two separate issues. First of all, theoretical predictions for the statistical weights are found to be poorly correlated with the statistics of visits by turbulent flow to the neighborhoods of individual RPOs. Second, on accessible time scales, turbulent flow shadows multiple RPOs without ever coming particularly close to any of them. |
Tuesday, November 23, 2021 1:58PM - 2:11PM |
T07.00007: Modulation theory for multidimensional gravity soliton interactions in the ocean Samuel Ryskamp, Mark A Hoefer, Gino Biondini, Michelle D Maiden Gravity solitons are high energy waves that are ubiquitous in shallow water, plasmas, and internal waves. Although transversely extended line solitons can be studied as exact solutions to the Kadomtsev-Petviashvili (KP) equation, a two-dimensional generalization of the Korteweg-de Vries equation, no general analytical methods for the evolution of their interactions and modulations have been found. This talk will utilize KP soliton modulation theory to model various interactions, such as a soliton emerging from a channel and a soliton incident upon an oblique corner. By interpreting these scenarios as Riemann problems in the modulation variables, we obtain analytical descriptions for line soliton dynamics that are both tractable and numerically verified. Some noteworthy results include a new interpretation of Mach reflection and the discovery of a related phenomenon called Mach expansion. |
Tuesday, November 23, 2021 2:11PM - 2:24PM |
T07.00008: FTLE of optimally controlled agents in unsteady flow fields. Kartik Krishna, Steven L Brunton, Zhuoyuan Song Finite-time Lyapunov exponents (FTLE) are used to compute Lagrangian coherent structures of unsteady fluid flow fields. These coherent structures can be used to understand the transport mechanisms of passive tracers advecting with the flow. However, many of the vehicles and mobile sensors we wish to deploy in the ocean or atmosphere are actuated, and some form of intelligent trajectory planning (such as model predictive control) is often adopted to move them optimally in the dynamically changing background flow. In this work, we investigate the use of FTLE on such controlled agents to gain insight into optimal transport routes for navigation in known unsteady flows. We find that these controlled FTLE (cFTLE) coherent structures separate the flow field into different regions based on the cost of transport to the goal location. These separatrices are functions of the planning algorithm's hyper-parameters, such as the optimization time horizon, the maximum actuation amplitude, and the cost of actuation. We can use this information to gain insight into effective deployment locations for mobile agents (which have limitations on actuation and energy capacity) to traverse the ocean or atmosphere. |
Tuesday, November 23, 2021 2:24PM - 2:37PM |
T07.00009: Linearized analyses of fluid flows from nonlinear simulation data Benjamin Herrmann, Peter J Baddoo, Steven L Brunton, Beverley J McKeon The Dynamic Mode Decomposition (DMD) has been consolidated as a basic tool for data-driven analysis of fluid flows, allowing simultaneous identification of coherent structures and their dynamics from time-resolved measurements. However, with a linear regression at its core, DMD is unable to produce accurate models from recordings of dynamics that are inherently nonlinear, such as the response to large perturbations and the evolution on chaotic attractors. Fortunately, the Linear and Nonlinear Disambiguation Optimization (LANDO) enables DMD-like, data-driven analysis of high-dimensional dynamical systems that is robust to strong nonlinearities. Leveraging kernel regression, LANDO produces an accurate model for the evolution of the system, isolates the purely nonlinear contributions to the dynamics in the data, and identifies interpretable coherent structures associated with the linear part of the dynamics. We explore the potential of LANDO to perform linearized analyses of fluid flows, such as stability, Floquet, transient growth, and resolvent analysis, from snapshots of nonlinear simulations. |
Tuesday, November 23, 2021 2:37PM - 2:50PM |
T07.00010: Recurrence-based identification of coherent motion from very-sparse Lagrangian particle trajectories Giovanni Iacobello, Frieder Kaiser, David E Rival The identification of coherent motion is a fundamental issue for the characterization and control of fluid flows. So far, several techniques have been proposed to extract coherent motion from a (turbulent) flow, either adopting an Eulerian or a Lagrangian framework. In a large variety of cases, e.g. atmospheric or oceanic flows, the Lagrangian viewpoint represents a more suitable choice for the spatio-temporal investigation of the flow. However, in practice, only a limited number of tracers is typically available, leading to (very-)sparse Lagrangian datasets. In this work, we exploit a recurrence network strategy to identify coherent motion from very-sparse particle trajectories. Specifically, a network is built on a single tracer trajectory, adopting a distance-based criterion of recurrence. The proposed methodology is objective (i.e., frame-independent), applicable to 2D and 3D data, and can be used for broken trajectories (as typically obtained in experiments via particle tracking tools). The recurrence-based approach is tested on a set of numerical and experimental test cases, showing its potential in identifying coherent motion for very-sparse particle trajectories. |
Tuesday, November 23, 2021 2:50PM - 3:03PM Not Participating |
T07.00011: Phase Proper Orthogonal Decomposition of numerical data Yisheng Zhang, Azur Hodzic, Fabien Evrard, Clara M Velte We present a Proper Orthogonal Decomposition (POD) technique for describing the four-dimensional (spatial and temporal) behavior of unsteady turbulent flow. We name this technique Phase Proper Orthogonal Decomposition (Phase POD), which does not assume steady or periodic flow. As Phase POD includes all temporal-spatial information in the modes, purely spatial POD[1] and Spectral POD[2] are special cases of Phase POD. The modes of Phase POD will have the energy optimality including the temporal properties. We illustrate the method on an example of a unsteady cavity flow. |
Tuesday, November 23, 2021 3:03PM - 3:16PM |
T07.00012: Sparse Sensor-based Flow Estimation Using Artificial Neural Networks and Spectral Proper Orthogonal Decomposition Henrique De Lima Gambassi, Paul Ziade, Christopher R Morton The application of Artificial Neural Networks (ANNs) in developing sensor-based estimators for unsteady turbulent flows has become an active area of research over the last decade. One of the challenges in this area is in the selection of an optimal low-dimensional subspace which enables the ANN to reconstruct relevant spatiotemporal dynamics in the flow and avoid overfitting data to the underlying stochastic fluctuations. The energetically optimal Proper Orthogonal Decomposition (POD) and the spectrally pure Discrete Fourier Transform (DFT) both have shown promising results, however, these algorithms have intrinsic limitations. These limitations affect how well the physics of different flows can be represented in a sparse basis. The present study aims at demonstrating that for certain flows, the versatile time-domain Spectral Proper Orthogonal Decomposition (SPOD, M. Sieber et al., J. Fluid Mech. (2016), vol. 792, pp.798-828) provides an improved basis compared to the traditional methods (POD, DFT) for neural networks to perform a sensor-based flow estimation task. In the study, the SPOD basis is compared to the other candidate bases (POD, DFT), and the differences in performance of the neural networks are linked to the features that are captured or suppressed in the different mode spaces. |
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