Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session D1: Nonlinear Dynamics: Coherent Structures INonlinear Shear layer

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Chair: Thomas Solomon, Bucknell University Room: 401 
Sunday, November 19, 2017 2:15PM  2:28PM 
D1.00001: Resolvent analysis of exact coherent solutions Kevin Rosenberg, Beverley McKeon Exact coherent solutions have been hypothesized to constitute the statespace skeleton of turbulent trajectories and thus are of interest as a means to better understand the underlying dynamics of turbulent flows. An asymptotic description of how these types of solutions selfsustain was provided by Hall \& Sherwin (JFM, 2010). Here we offer a fullynonlinear perspective on the selfsustainment of these solutions in terms of triadic scale interactions and use the resolvent framework of McKeon \& Sharma (JFM, 2010) to interpret these results from an input/output point of view. We analyze traveling wave solutions and periodic orbits in channel flow, and demonstrate how resolvent analysis can be used to obtain lowdimensional representations of these flows. [Preview Abstract] 
Sunday, November 19, 2017 2:28PM  2:41PM 
D1.00002: Burning invariant manifolds for reaction fronts in threedimensional fluid flows Kevin Mitchell, Tom Solomon The geometry of reaction fronts that propagate in fully threedimensional (3D) fluid flows is studied using the tools of dynamical systems theory. The evolution of an infinitesimal front element is modeled as a sixdimensional ODEthree dimensions for the position of the front element and three for the orientation of its unit normal. This generalizes an earlier approach to understanding front propagation in twodimensional (2D) fluid flows. As in 2D, the 3D system exhibits prominent \emph{burning invariant manifolds} (BIMs). In 3D, BIMs are twodimensional dynamically defined surfaces that form oneway barriers to the propagation of reaction fronts within the fluid. Due to the third dimension, BIMs in 3D exhibit a richer topology than their cousins in 2D. In particular, whereas BIMs in both 2D and 3D can originate from fixed points of the dynamics, BIMs in 3D can also originate from limit cycles. Such BIMs form robust tubelike channels that guide and constrain the evolution of the front within the bulk of the fluid. [Preview Abstract] 
Sunday, November 19, 2017 2:41PM  2:54PM 
D1.00003: Experimental studies of oneway reaction front barriers in threedimensional vortex flows Joanie Gannon, Minh Doan, JJ Simons, Kevin Mitchell, Tom Solomon We present results of experimental studies of the evolution of the excitable, Ruthenium (Ru)catalyzed, BelousovZhabotinsky (BZ) reaction in a threedimensional (3D) flow composed of the superposition of horizontal and vertical vortex chains. The reaction fronts are imaged in 3D with a scanning, laserinduced fluorescence technique that takes advantage of the differential fluoresence of the Ruthenium indicated at the front. When the horizontal and vertical vortex chains are lined up, a dominant scroll structure is observed that acts as a oneway barrier blocking fronts propagating across vortex boundaries and into vortex centers. A second, quartertube barrier is observed along the edges of the unit cell. When the vortices are shifted relative to each other, tubelike barriers are observed in the interior. All of these barriers are compared with {\em burning invariant manifolds} predicted from a 6D set of differential equations describing the evolution of front elements in the flow. [Preview Abstract] 
Sunday, November 19, 2017 2:54PM  3:07PM 
D1.00004: Local Learning Strategies for Wake Identification Brendan Colvert, Mohamad Alsalman, Eva Kanso Swimming agents, biological and engineered alike, must navigate the underwater environment to survive. Tasks such as autonomous navigation, foraging, mating, and predation require the ability to extract critical cues from the hydrodynamic environment. A substantial body of evidence supports the hypothesis that biological systems leverage local sensing modalities, including flow sensing, to gain knowledge of their global surroundings. The nonlinear nature and high degree of complexity of fluid dynamics makes the development of algorithms for implementing localized sensing in bioinspired engineering systems essentially intractable for many systems of practical interest. In this work, we use techniques from machine learning for training a bioinspired swimmer to learn from its environment. We demonstrate the efficacy of this strategy by learning how to sense global characteristics of the wakes of other swimmers measured only from local sensory information. We conclude by commenting on the advantages and limitations of this datadriven, machine learning approach and its potential impact on broader applications in underwater sensing and navigation. [Preview Abstract] 
Sunday, November 19, 2017 3:07PM  3:20PM 
D1.00005: Layer formation and localisation in spanwise stratified plane Couette flow. Dan Lucas, C.P. Caulfield, Rich Kerswell, John Taylor Recent research has shed light on the role of coherent structures in forming layers when vertically stably stratified turbulence is forced with horizontal shear (https://arxiv.org/abs/1701.05406). In the current work we investigate the role of stable stratification in modifying coherent structures in plane Couette flow when the mean shear is horizontal i.e. gravity points in the (vertical) spanwise direction. Direct numerical simulations reveal near wall layering and associated new mean flows in the form of flattened streamwise rolls. Stratification is also found to inhibit the vertical growth of localised structures, meaning that spanwise localisation in the form of deep relatively wellmixed layers are found which fill the wallnormal (horizontal) and streamwise extents. We also use this geometry to investigate the influence of stratification on the growth and localization of isolated turbulent spots using a recently developed adaptive control procedure (Taylor et. al. 2016 J. Fluid Mech. 808). [Preview Abstract] 
Sunday, November 19, 2017 3:20PM  3:33PM 
D1.00006: Interactions of solitary waves and compression/expansion waves in coreannular flows Michelle Maiden, Dalton Anderson, Gennady El, Nevil Franco, Mark Hoefer The nonlinear hydrodynamics of an initial step leads to the formation of rarefaction waves and dispersive shock waves in dispersive media. Another hallmark of these media is the soliton, a localized traveling wave whose speed is amplitude dependent. Although compression/expansion waves and solitons have been wellstudied individually, there has been no mathematical description of their interaction. In this talk, the interaction of solitons and shock/rarefaction waves for interfacial waves in viscous, miscible coreannular flows are modeled mathematically and explored experimentally. If the interior fluid is continuously injected, a deformable conduit forms whose interfacial dynamics are welldescribed by a scalar, dispersive nonlinear partial differential equation. The main focus is on interactions of solitons with dispersive shock waves and rarefaction waves. Theory predicts that a soliton can either be transmitted through or trapped by the extended hydrodynamic state. The notion of reciprocity is introduced whereby a soliton interacts with a shock wave in a reciprocal or dual fashion as with the rarefaction. Soliton reciprocity, trapping, and transmission are observed experimentally and are found to agree with the modulation theory and numerical simulations. [Preview Abstract] 
Sunday, November 19, 2017 3:33PM  3:46PM 
D1.00007: Phasespace dynamics of opposition control in wallbounded turbulent flows Yongyun Hwang, Joseph Ibrahim, Qiang Yang, Patrick Doohan The phasespace dynamics of wallbounded shear flow in the presence of opposition control is explored by examining the behaviours of a pair of nonlinear equilibrium solutions (exact coherent structures), edge state and life time of turbulence at low Reynolds numbers. While the control modifies statistics and phasespace location of the edge state and the lowerbranch equilibrium solution very little, it is also found to regularise the periodic orbit on the edge state by reverting a perioddoubling bifurcation. Only the upperbranch equilibrium solution and mean turbulent state are significantly modified by the control, and, in phase space, they gradually approach the edge state on increasing the control gain. It is found that this behaviour results in a significant reduction of the life time of turbulence, indicating that the opposition control significantly increases the probability that the turbulent solution trajectory passes through the edge state. Finally, it is shown that the opposition control increases the critical Reynolds number of the onset of the equilibrium solutions, indicating its capability of transition delay. [Preview Abstract] 
Sunday, November 19, 2017 3:46PM  3:59PM 
D1.00008: Modal Structures in flow past a cylinder Mohammad Murshed With the advent of data, there have been opportunities to apply formalism to detect patterns or simple relations. For instance, a phenomenon can be defined through a partial differential equation which may not be very useful right away, whereas a formula for the evolution of a primary variable may be interpreted quite easily. Having access to data is not enough to move on since doing advanced linear algebra can put strain on the way computations are being done. A canonical problem in the field of aerodynamics is the transient flow past a cylinder where the viscosity can be adjusted to set the Reynolds number (Re). We observe the effect of the critical Re on the certain modes of behavior in time scale. A 2Dvelocity field works as an input to analyze the modal structure of the flow using the Proper Orthogonal Decomposition and Koopman Mode/Dynamic Mode Decomposition. This will enable prediction of the solution further in time (taking into account the dependence on Re) and help us evaluate and discuss the associated error in the mechanism. [Preview Abstract] 
Sunday, November 19, 2017 3:59PM  4:12PM 
D1.00009: Introducing Etec: Ensemblebased Topological Entropy Calculation Eric Roberts, Spencer Smith, Suzanne Sindi, Kevin Smith Topological entropy is a measurement of orbit complexity in a dynamical system that can be estimated in 2D by embedding an initial material curve $L_0$ in the fluid and estimating its growth under the evolution of the flow. This growth is given by $L(t) ~ = ~ L_0~e^{ht}, $ where $L(t)$ is the length of the curve as a function of $t$ and $h$ is the topological entropy. In order to develop a method for computing Eq. (1) that will efficiently scale up in both system size and modeling time, one must be clever about extracting the maximum information from the limited trajectories available. The relative motion of trajectories through phase space encodes global information that is not contained in any individual trajectory. That is, extra information is "hiding" in an ensemble of classical trajectories, which is not exploited in a trajectorybytrajectory approach. Using tools from computational geometry, we introduce a new algorithm designed to take advantage of such additional information that requires only potentially sparse sets of particle trajectories as input and no reliance on any detailed knowledge of the velocity field: the $\textbf{E}$nsembleBased $\textbf{T}$opological $\textbf{E}$ntropy $\textbf{C}$alculation, or Etec. [Preview Abstract] 
Sunday, November 19, 2017 4:12PM  4:25PM 
D1.00010: Coherent Structure Detection using Persistent Homology and other Topological Tools Spencer Smith, Eric Roberts, Suzanne Sindi, Kevin Mitchell For nonautonomous, aperiodic fluid flows, coherent structures help organize the dynamics, much as invariant manifolds and periodic orbits do for autonomous or periodic systems. The prevalence of such flows in nature and industry has motivated many successful techniques for defining and detecting coherent structures. However, often these approaches require very fine trajectory data to reconstruct velocity fields and compute CauchyGreentensorrelated quantities. We use topological techniques to help detect coherent trajectory sets in relatively sparse 2D advection problems. More specifically, we have developed a homotopybased algorithm, the ensemblebased topological entropy calculation (Etec), which assigns to each edge in an initial triangulation of advected points a topologically forced lower bound on its future stretching rate. The triangulation and its weighted edges allow us to analyze flows using persistent homology. This topological data analysis tool detects clusters and loops in the triangulation that are robust in the presence of noise and in this case correspond to coherent trajectory sets. [Preview Abstract] 
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