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 L01: Nonlinear Dynamics: Coherent Structures II |
Hide Abstracts |
Chair: George Haller, ETH Zurich Room: Georgia World Congress Center B201 |
Monday, November 19, 2018 4:05PM - 4:18PM |
L01.00001: What makes the boundary of uniform concentration zones ? Willem van de Water, Jerke Eisma, Jerry Westerweel, Daniel Seewai Tam A plume of pollutant that spreads in a turbulent boundary layer does not mix homogeneously. Large regions remain with little variation of the concentration inside, separated by sharp boundaries where the concentration jumps: uniform concentration zones. In experiments on a turbulent boundary layer in a water tunnel we simultaneously measure the full three-dimensional velocity field using tomographic PIV and the concentration of fluorescent dye that comes from a point source using LIF. |
Monday, November 19, 2018 4:18PM - 4:31PM |
L01.00002: Coherent structures, instabilities, and the arrow of time Douglas H Kelley, Jeffrey R Tithof, Balachandra Suri, Michael F Schatz, Roman O Grigoriev In fluid dynamics, viscosity sets the arrow of time: if viscosity is nonnegative, the Second Law of Thermodynamics is satisfied. But time-asymmetry can still be small, as in the famous demonstration by G. I. Taylor, if the nonlinear term of the Navier-Stokes equation is negligible. Nonlinearities matter most, in the sense of sensitive dependence on initial conditions, in regions where finite-time Lyapunov exponents are largest. Those same regions are home to Lagrangian Coherent Structures (LCS), the flow's most important barriers to mixing. We present experiments and simulations showing that the motion of forward-time LCS differs from that of backward-time LCS, as in prior work. Varying flow speed, we show that time-asymmetry of LCS motion is nearly zero for steady flow and increases with Reynolds number. In fact, time-asymmetry jumps discontinuously at the Reynolds number where an instability initiates periodic flow, and jumps again where periodicity gives way to chaos. Our results suggest that time-asymmetry is often driven by interactions between nonlinearities and viscosity, and are relevant to attempts to make LCS predictive, not merely descriptive, since attracting LCS are less predictable than repelling LCS. |
Monday, November 19, 2018 4:31PM - 4:44PM |
L01.00003: Local linearity, coherent structures, and scale-to-scale coupling in two-dimensional flow. Lei Fang, Sanjeeva Balasuriya, Nicholas Ouellette Turbulent and other nonlinear flows are highly complex and time dependent, but are not fully random. To capture this spatiotemporal coherence, We introduce the idea of a Linear Neighborhood (LN), defined as a region in an arbitrary flow field where the velocity gradient varies slowly in space over a finite time. Thus, by definition, the flow in a LN can be approximated arbitrarily well by only a subset of the trajectories in LN. Slow spatiotemporal variation also allows short-time prediction of the flow. We demonstrate that these LNs are computable in real data using experimental measurements from a quasi-two-dimensional turbulent flow, and find support for our theoretical arguments. We also show that our kinematically defined LNs have an additional dynamical significance, in that the scale-to-scale spectral energy flux that is a hallmark of turbulent flows behaves differently inside the LNs. Our results add additional support to the conjecture that turbulent flows locally tend to transport energy and momentum in space or in scale but not both simultaneously. |
Monday, November 19, 2018 4:44PM - 4:57PM |
L01.00004: Material Barriers to Diffusive and Stochastic Transport George Haller, Daniel Karrasch, Florian Kogelbauer Observations of tracer transport in fluids generally reveal highly complex patterns shaped by an intricate network of transport barriers. The elements of this network appear to be universal for small diffusivities, independent of the tracer and its initial distribution. In this talk, I discuss a mathematical theory for weakly diffusive tracers that predicts transport barriers and enhancers solely from the flow velocity, without reliance on diffusive simulations. The theory also extends to particle motion under uncertainties, eliminating the need for Monte-Carlo simulations in detecting stochastic transport barriers. I illustrate the results on Rayleigh-Benard convection simulation and on satellite-inferred ocean current data. |
Monday, November 19, 2018 4:57PM - 5:10PM |
L01.00005: Automated computation of material barriers to diffusive and stochastic transport Stergios Katsanoulis, Mattia Serra, George Haller Lagrangian coherent structures (LCS) are distinguished, time-evolving surfaces that shape conservative tracer patterns in complex dynamical systems. The objective (observer-independent) identification of such structures has recently been extended to uncover the material skeletons of diffusive and stochastic tracer patterns. In this extended theory, diffusion barriers are identified as material surfaces that inhibit the diffusion of passive scalars more than neighbouring surfaces do. Here, we describe a computational algorithm based on these new results. The algorithm offers a fully automated detection of conservative, diffusive and stochastic transport barriers without reliance on user input or fine-tuning of parameters, as other coherent-structure-detection algorithms typically do. Moreover, we extend the new, diffusive LCS theory to uncover objectively defined instantaneous (Eulerian) barriers to diffusive transport. We also introduce a publicly available Matlab graphical user interface (GUI) that implements all these results for general, two-dimensional unsteady flow data. We close by demonstrating the use of this GUI on a satellite-based oceanic surface velocity data set. |
Monday, November 19, 2018 5:10PM - 5:23PM |
L01.00006: Prediction of closed diffusion barriers in axisymmetric Taylor-Couette flow Daniel Feldmann, Stergios Katsanoulis, George Haller, Marc Avila Reliable identification of Lagrangian coherent structures (LCS) plays a key role in understanding and predicting how the transport of mass and momentum organises itself in turbulent fluid flows. A newly developed method (Haller et al. PNAS, subm.) enables us to detect elliptic LCS as vortex-type barriers to diffusive transport. These diffusion barriers (DB) are constructed mathematically as closed material surfaces that block the diffusion of passive scalars more than any other neighbouring surface. Here, we apply this method for the first time to axisymmetric Taylor-Couette flow. By means of direct numerical simulations we generated dense time series of the full velocity field for a substantial range of Re ≤ 20000 using our pseudo-spectral Navier-Stokes solver nsCouette (Shi et al. Comp. Fluids 106, 2015). Here Re = ^{du}/_{ν} is the Reynolds number based on the gap width d, viscosity ν and rotation speed u of the inner cylinder, whereas the outer cylinder is kept stationary. Thus, we were able to identify closed diffusion barriers and track their individual evolution in time for different realisations of the instantaneous flow field. Furthermore, we track how DB change and disappear as Re increases. |
Monday, November 19, 2018 5:23PM - 5:36PM |
L01.00007: Model parameter estimation using coherent structure coloring Kristy Schlueter-Kuck, John O. Dabiri Lagrangian data assimilation is a complex problem in oceanic and atmospheric modeling. Tracking drifters in large-scale geophysical flows involves uncertainty in drifter location, complex inertial effects, and other factors which make comparing them to simulated Lagrangian trajectories from numerical models extremely challenging. Additionally, chaotic advection inherent in these flows tends to separate closely-spaced tracer particles, making error metrics based on drifter displacements unsuitable for estimating model parameters. We propose using error in the coherent structure coloring (CSC) field, a spatial representation of the underlying coherent patterns in a flow, to assess model skill. We show that error in the CSC field can be used to accurately determine multiple unknown model parameters simultaneously whereas an error metric based on error in drifter displacement fails. The effectiveness of this method suggests that Lagrangian data assimilation for multi-parameter oceanic and atmospheric models would benefit from a similar approach. |
Monday, November 19, 2018 5:36PM - 5:49PM |
L01.00008: Unsupervised machine learning for coherent structure identification Brooke E. Husic, Kristy L. Schlueter-Kuck, John O. Dabiri The clustering of fluid particle trajectories into coherent structures often requires a priori assumptions about the nature of the coherent subgroups. We present a new method, simultaneous Coherent Structure Coloring (sCSC), which performs unsupervised learning on measured or simulated Lagrangian flow trajectories without anticipating the underlying structure of the data. Unlike common methods, rather than clustering similar states (i.e., particle trajectories), sCSC separates the most dissimilar states via a generalized eigenvalue problem. The set of eigenvector solutions are bifurcated and sequentially applied to the data, yielding a binary dendrogram representation. The number of coherent structures emerges naturally, since many fewer branches are occupied than is combinatorically possible. We demonstrate that sCSC can identify the structures governing fluid transport in both theoretical models and laboratory measurements with two orders of magnitude less data than existing methods and no a priori assumptions. |
Monday, November 19, 2018 5:49PM - 6:02PM |
L01.00009: Experimental comparison of coherent structures methods applied to oceanic flows Margaux Filippi, Michael Allshouse, Siavash Ameli, Patrick Haley, Chinmay Kulkarni, Pierre Lermusiaux, Thomas Peacock, Irina Rypina, Mattia Serra Based on velocity outputs from numerical model forecasts and their subsequent processing with Lagrangian Coherent Structures (LCS) methods, a series of field experiments was conducted offshore Martha’s Vineyard to specifically target the predicted LCS, with the goal of testing the reliability and utility of the approach. The resulting surface drifter trajectories were compared to the analyses of several Lagrangian processing methods, which were used on both the forecast model data for experimental design and the hindcast model data to explain the observed behaviors of drifters. The different LCS methods used include the Finite-Time Lyapunov Exponent method, the encounter volume method and clustering methods, such as fuzzy c-means and spectral clustering. The Objective Eulerian Coherent Structure (OECS) method was also tested in the field. |
Monday, November 19, 2018 6:02PM - 6:15PM |
L01.00010: Dynamics and Interactions of Truncated, Two-Dimensional Line Solitons in Shallow Water Mark Hoefer, Michelle D Maiden, Gino Biondini It is well-known that the Kadomtsev-Petviashvili II (KP-II) equation—an asymptotic model of weakly nonlinear, shallow water gravity waves with weak transverse variation—admits stable, two-dimensional, line soliton solutions characterized by their amplitude and slope. Their dynamics subject to modulation, e.g., truncation and bending, are studied utilizing the soliton limit of the recently derived KP-Whitham modulation equations. A Riemann invariant form for the modulation equations—a system of two hyperbolic equations in two space dimensions and time for the soliton's amplitude and slope—is identified that enables exact solution methods including simple waves and hodograph techniques. This theory is used to describe the evolution of truncated solitons: an isolated line soliton segment and the interaction of two semi-infinite line solitons. The results compare favorably with direct numerical simulation and have application to near-shore nonlinear wave dynamics. |
Monday, November 19, 2018 6:15PM - 6:28PM |
L01.00011: Oblique dispersive shock waves in steady supercritical shallow water flow Patrick Sprenger, Adam Binswanger, Mark Hoefer Dispersive shock waves (DSWs) are universal structures arising in hydrodynamic nonlinear wave systems where dissipation is negligible with respect to wave dispersion. DSWs have recently been studied in great detail, due to their ubiquity in physical systems--examples of which range from ultra-cold superfluids at micron scales to atmospheric flows at kilometer scales. Here we consider steady, oblique DSWs generated by deflecting a supercritical shallow water flow past a thin wedge. The boundary value problem associated with the fluid flow can be recast as an initial value problem of a steady Korteweg-de Vries (KdV) equation via a multi-scale asymptotic expansion where one spatial dimension is time-like. For sufficiently shallow flow, surface tension forces are in balance with gravity and the KdV model equation must be adjusted to include a fifth order dispersive term. The high order model equation gives predictions for a bifurcation in the DSW structure as the flow depth passes through approximately 5 mm because of the higher order dispersion. Here, we will detail the structure of DSWs predicted from the approximate model equation using Whitham modulation theory and numerical simulations. The next talk will discuss an experiment where this theory can be tested. |
Monday, November 19, 2018 6:28PM - 6:41PM |
L01.00012: Experimental Investigation of Oblique Dispersive Shock Waves in Steady Supercritical Shallow Water Flow Adam Lewis Binswanger, Patrick Sprenger, Mark Hoefer A shallow water experiment is implemented in which a sluice gate controls a supercritical flow that is deflected by a slender wedge. Due to surface wave dispersion, the ensuing steady structure is a spatially extended, oscillatory pattern referred to as an oblique dispersive shock wave (DSW), which is a modulated nonlinear wavetrain limiting to an oblique solitary wave at the trailing edge closest to the wedge. Appropriate variation of water depth, flow speed, and deflection angle results in a bifurcation in the flow pattern. The Bond number B, measuring the effects of surface tension relative to gravity, characterizes the bifurcation. The quantity B = 1/3, corresponding to a fluid depth of approximately 5 mm, is the bifurcation point, where there is a transition between classical and non-classical DSW profiles. They are differentiated by monotonicity in their trailing solitary wave edges and the nonlinear wavetrain that ensues. Surface water wave profiles are measured via the Fourier transform profilometry technique and the reconstructed surface profiles are compared with theoretical predictions for the DSW structure as presented in a companion talk. |
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. |
© 2019 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