Bulletin of the American Physical Society
75th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2022; Indiana Convention Center, Indianapolis, Indiana.
Session Q21: Nonlinear Dynamics: Resolvents, Coherent Structures and Transition |
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Chair: Robert Martinuzzi, University of Calgary Room: 207 |
Monday, November 21, 2022 1:25PM - 1:38PM |
Q21.00001: Simultaneous shadowing of multiple Exact Coherent Structures in experimental Taylor-Couette flow Wesley Toler, Christopher J. Crowley, Joshua L. Pughe-Sanford, Roman O Grigoriev, Michael F Schatz Eberhard Hopf first envisioned turbulent flow as being comprised of a sequence of special solutions of the governing equations, often referred to as Exact Coherent Structures (ECS). In this picture, turbulent flow co-evolves with, or "shadows", one such solution for a time; then a different ECS; and so on. This qualitative picture has recently been confirmed quantitatively in experimental Taylor-Couette flow. We demonstrate that this three-dimensional turbulent flow shadows, episodically but repeatedly, the spatial and temporal structure of multiple ECSs. We also unexpectedly observe that more than one ECS may be shadowed simultaneously by the turbulent flow. We explain this phenomenon in part through the relation of certain ECSs via bifurcations, as well as the similarity of segments of unrelated ECSs. |
Monday, November 21, 2022 1:38PM - 1:51PM |
Q21.00002: Exploring the connections between exact coherent structures and attractors in active nematic channel flow Caleb Wagner, Rumayel Pallock, Michael M Norton, Jae Sung Park, Piyush Grover Exact Coherent Structures (ECS) are stationary, periodic, quasiperiodic, or traveling wave solutions of the governing equations that, together with their invariant manifolds, serve as an organizing template of the dynamics of a fluid system. Active nematics is a class of active fluids that exhibits rich dynamical behavior, including spontaneous flows, periodic defect dynamics, and chaotic `active turbulence'. In this work, we compute over 100 ECSs in a 2D active nematic channel flow system, and provide evidence that these ECSs are shadowed by typical trajectories of the system. We also discuss the presence of robust heteroclinic cycles in the system that cycle between the two opposite flowing unidirectional flow states, as well as several other exotic trajectories that can be explained using the ECS framework. |
Monday, November 21, 2022 1:51PM - 2:04PM |
Q21.00003: Global resolvent analysis of three-dimensional jets using randomized linear algebra and time stepping Ali Farghadan, Eduardo Martini, André Cavalieri, Aaron S Towne Resolvent analysis is a powerful tool for modeling coherent structures in turbulent flows. Resolvent forcing and response modes are defined in terms of the singular value decomposition (SVD) of the resolvent operator, but the computational cost of computing these modes scales poorly with problem size and becomes computationally expensive for large systems, typically limiting resolvent analysis to flows with one or two inhomogeneous directions. Recently, we have developed an improved algorithm (called RSVDt) by combining randomized SVD with an optimized direct and adjoint time-stepping routine, which achieves linear cost scaling with problem size and enables efficient resolvent analysis of three-dimensional flows. Time stepping constitutes the majority of the cost of our algorithm, and we propose a new approach to minimize this cost by eliminating undesired transients that otherwise lengthen the time interval to be computed. We use a series of jets to demonstrate our algorithm. First, we use two jet models to show that RSVDt decreases memory and CPU cost by two and three orders of magnitude, respectively, compared to other state-of-the-art algorithms. Second, we use RSVDt to compute resolvent modes for a previously intractable three-dimensional jet and use this new capability to explore the impact of steady streaks on Kelvin-Helmholtz wavepackets. |
Monday, November 21, 2022 2:04PM - 2:17PM |
Q21.00004: From resolvent to Gramians: forcing and response modes for control Benjamin Herrmann, Peter J Baddoo, Richard Semaan, Steven L Brunton, Beverley J McKeon During the last decade, forcing and response modes produced by resolvent analysis have promised to have an impact on flow control applications due to their potential to guide sensor and actuator placement and design. However, resolvent modes are frequency-dependent, which, although responsible for their success in identifying scale interactions in turbulence, complicates their use for control purposes. In this work, we seek orthogonal bases of forcing and response modes that are the most responsive and receptive, respectively, across all frequencies. We show that these frequency-independent bases of representative resolvent modes are given by the eigenvectors of the observability and controllability Gramians of the system considering full state inputs and outputs. We present several numerical examples where we leverage these eigenbases by building orthogonal or interpolatory projectors. Forcing modes are used to identify dynamically relevant disturbances, to place point sensors to measure disturbances, and to design spatially-distributed and spatially-localized actuators for feedforward control. Response modes are used for point sensor placement aiming at flow reconstruction. |
Monday, November 21, 2022 2:17PM - 2:30PM |
Q21.00005: Information-theoretic quantification of causality in turbulent flows Yuenong Ling, Gonzalo Arranz, Adrian Lozano-Duran Understanding causality among quantities of interest in turbulent flows is essential for physical understanding, modeling, and control. In this talk, we discuss a new method to quantify causality in turbulence based on information fluxes. The main properties of the method and its suitability for quantifying causality are highlighted. The method is non-intrusive and only requires the time history of the flow, which is convenient both computationally and experimentally. We leveraged the approach to investigate the causality of the energy cascade in isotropic turbulence. The results are validated against (the more expensive) causality with interventions, in which the system is modified, and the consequences are measured. |
Monday, November 21, 2022 2:30PM - 2:43PM |
Q21.00006: Deformation of FTLE ridges under the action of control in unsteady fluid flows Kartik Krishna, Steven L Brunton, Zhuoyuan Song Finite-time Lyapunov Exponent fields allow us to visualize transport barriers and regions of strong attraction or repulsion for passive particles in an unsteady fluid flow. It is also possible to extract FTLE from data generated by active agents that use actuation to move through the flow. The effect of actuation and control may be viewed as resulting in a new effective background vector field in which the active agent appears to be a passive particle. Therefore, when FTLE is computed for active agents, the resulting control FTLE (cFTLE) field deviates from the passive FTLE field. In our work, we investigate the deformation of the cFTLE field from the passive FTLE on agents using model predictive control (MPC) to move through the flow. In particular, we investigate how changes in the control parameters produce deformations in the cFTLE ridges; these parameters include time horizon, energy penalty, and location of the goal target. These results could be useful in the context of agents navigating in the ocean, for example to generate high-level control policies or to decide where to deploy agents. |
Monday, November 21, 2022 2:43PM - 2:56PM |
Q21.00007: Efficient tensor-based sensor placement for turbulent flow reconstructions Arvind K Saibaba, Mohammad M Farazmand This talk will address the question of determining sensor locations to optimally place a limited number of sensors, from which the collected data can be used to accurately recover the turbulent flow fields. Previous work has used a basis obtained using proper orthogonal decomposition to approximate the flow field and used row subset selection to obtain near-optimal interpolation points that determine sensor locations. However, this approach does not exploit the inherent multidimensional structure of the flow fields. To address this, we use a tensor-based approach to approximate the flow field and obtain near-optimal interpolation points along each tensor mode. The resulting approach has much lower storage requirements and is often more accurate for a comparable number of sensors. Numerical experiments on a variety of fluid problems, such as the Kolmogorov flow and seasurface temperature, will illustrate the performance of the proposed methods. |
Monday, November 21, 2022 2:56PM - 3:09PM |
Q21.00008: Resolvent analysis of turbulent pipe flow laden with low-inertia particles Rasmus K Schlander, Stelios Rigopoulos, George Papadakis We extend the resolvent framework to turbulent flows laden with low-inertia particles. The particle velocities are modelled using the equilibrium Eulerian model, which is assumed to be valid for Stokes numbers up to 1. We analyse a vertical turbulent pipe flow with Reynolds number equal to 5300 based on diameter and bulk velocity, Froude numbers F r = −4, −0.4, 0.4, 4 and Stokes numbers St+ = 0−1. A direct numerical simulation (DNS) for a pipe with a length of 7.5 diameters is performed with the particles released uniformly at the inlet. The resolvent formulation can reproduce the physical phenomena observed in inertial particle flows, such as localized high concentration due to the vortical centrifuge effect, turbophoresis and gravitational effects. It also reveals that upward flow increases particle concentration in the log layer while downward flow increases concentration near the centre of the pipe: both features have been observed in previous Lagrangian simulations as well as experiments. The main effect of Stokes number is the amplification of the gain for resolvent modes with smaller streamwise wavelengths, resulting in an increase of the local scale clustering of particles and turbophoresis. |
Monday, November 21, 2022 3:09PM - 3:22PM |
Q21.00009: Large-scale circulation patterns rule the predictability of extreme events Alberto Vela-Martin, Marc Avila Extreme events in geophysical flows have a strong impact in human life and in diverse economical activities, and their |
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