Bulletin of the American Physical Society
73rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 65, Number 13
Sunday–Tuesday, November 22–24, 2020; Virtual, CT (Chicago time)
Session K06: Nonlinear Dynamics: General (8:45am  9:30am CST)Interactive On Demand

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K06.00001: Datadriven prediction of multistable systems from sparse measurements Mohammad Farazmand, Bryan Chu We develop a datadriven method for predicting the asymptotic behavior of nonlinear dynamical systems from sparse measurements. The systems of interest are described by partial differential equations (PDEs). As is usually the case in experiments, we assume that, at any given time, the state of the system can only be measured at a few sparse locations. To make accurate predictions, we formulate and solve a metriclearning optimization problem which promotes sparsity. The resulting metric determines the optimal points where measurements have to be made. The sparse measurements are then used in a clustering algorithm to predict the asymptotic state of the system. We illustrate the application of our method on a reactiondiffusion equation and show that it makes correct predictions more than 85\% of the time. [Preview Abstract] 

K06.00002: Mathematical model of gender bias in physics based on Galtung's triangle of violence Jennifer Pearce Johan Galtung proposed his theory of a triangle of violence in 1969 to explain how unseen violence hidden in the structures and culture of society can lead to the suppression of whole groups of people. In addition to direct violence, the other two points of the triangle are ``Structural violence'' and ``cultural violence''; indirect methods that dominant groups use to cause harm. This study uses an iterative map based on the well known LotkaVolterra equations to model the triangle of violence. The rvalue is used to represent structural violence, the interaction term between two populations represents cultural violence, and a stochastic term direct violence. Following an earlier study on the stochastic logistic map, the effective r value is calculated for two different interacting populations, dominant and nondominant. These can be used to calculate the total population and the percent of the total population for either group. Based on these results, we show that physics remains less diverse than other sciences because we graduate many fewer students on average than other sciences. [Preview Abstract] 

K06.00003: Nonlinear damping of sloshing motion caused by a piecewise linear contact line model Francois Gallaire, Alessandro Bongarzone We consider the sloshing motion in an idealized, twodimensional, container. We show that the presence of a brokenline piecewise linear contact line model relating the contact line velocity to the contact angle can be accounted for by a projection method on the eigenmode basis pertaining to each linear piece. We demonstrate that each slope discontinuity results in a loss of total energy and eventually contributes to the progressive nonlinear damping of the sloshing motion. [Preview Abstract] 

K06.00004: Low dimensional chaos in the solar magnetic cycle? Sumit Vashishtha, K.R. Sreenivasan The nature of dynamics underlying the solarcycle remains unclear. Considerable work has been done to understand if it is stochastic or has the character of deterministic chaos. In this talk, the sunspot series is analyzed using direct dynamical tests for deterministic chaos. A model based on the findings is constructed and the possible role of planetary influence on the solar cycle through a stochasticresonance like mechanism is explored. [Preview Abstract] 

K06.00005: Bifurcations and Chaos in the FluidStructure Interaction Dynamics of a Dipteran Flight Motor Chhote Lal Shah, Dipanjan Majumdar, Sunetra Sarkar The flapping dynamics of a Dipteran flight motor have been studied numerically by using a discrete forcing type Immersed Boundary Method (IBM) based inhouse fluidstructure interaction (FSI) solver at a Reynolds number of 100. A bifurcation study has been performed considering the amplitude of the wing actuation force as the control parameter. At lower values of the bifurcation parameters, the wake structures and the aerodynamic loads are similar to that of a rigid foil under the sinusoidal plunge. Further increment in the bifurcation parameter results in multiple harmonic frequencies in the structural response, which results in unequal speeds between the up and down strokes of the wing. Consequently, an asymmetric flowfield is obtained, which is also reflected in the aerodynamic loads. Eventually, the system response exhibits chaos at even higher values of the bifurcation parameter. Interesting dynamical behaviors such as quasiperiodicity, transient chaos, and intermittent transitions between chaotic and quasiperiodic states have also been observed. This study will help in understanding the physics during the transition in Dipteran flight, which can be crucial in developing the futuristic flappingwing micro air vehicles. [Preview Abstract] 

K06.00006: Predicting the onset of shockinduced buffet using Dynamic Mode Decomposition Sathsara Dias, Marko Budisic, Brian Helenbrook, Pat Piperni During transonic flight aircraft can experience a shockinduced buffet, an oscillation felt by the pilot and the aircraft structure which poses a significant constraint on the aircraft design. In idealized 2D flows buffet is linked to a Hopftype bifurcation, although realistic flow configurations additionally contain a range of background flow features. In this talk we show how Koopman analysis and Dynamic Mode Decomposition (DMD) techniques can be used to predict the onset of the buffet by tracking decay of transients in prebuffet simulations generated by a ReynoldsAveraged NavierStokes code on unstructured meshes. DMD algorithms decompose a sequence of snapshots into a sum of modes; to predict the buffet bifurcation we track the primary mode associated with the buffet across the threshold of stability. We demonstrate how the approach performs when applied to timeresolved simulations and simulations without physicallyaccurate timestepping. The results show that in the idealized timeresolved case the bifurcation could be predicted by tracking the change in time constants, although duration and resolution of input data affect the accuracy of the prediction. An additional challenge in realistic flows is identifying the primary mode among other components of the flow. [Preview Abstract] 

K06.00007: Topological entropy calculation in 2D fluid flows using limitedtime tracer particles Xiaolong Chen, Kevin Mitchell, Spencer Smith Topological entropy quantifies the complexity of 2D chaotic flows by measuring the stretching rate of a material curve. This quantity can be estimated by the trajectories of an ensemble of passive tracers, such as beads. Previous work has required these trajectories to persist for the full duration of experimental interest. However, it is common in experimentally tracked data for trajectories to begin and end at different times, either because trajectories have moved out of the focal plane, left the image domain, or have simply not been tracked properly from frame to frame. In this talk, we extend our previous methodthe ensemblebased topological entropy calculation (Etec)to accommodate such limitedtime trajectories. Through numerical simulation, we show that one can still compute an accurate topological entropy even when no single trajectory persists for the full duration of the time interval of interest. [Preview Abstract] 

K06.00008: Fluid Mixing using Braids on a Lattice Sierra Dunn, Spencer Smith Fluid mixing has many important applications, from predicting the behavior of microfluidic devices on the small scale to mitigating the spread of pollutants in the ocean on a larger scale. We often want to maximize mixing, such as when designing an efficient mixer for industrial use. We consider a specific model of mixing in two dimensions, in which stirring rods move the fluid around. To measure mixing, we track the stretching of material lines in the fluid. The exponential stretching rate of these lines over time quantifies the strength of mixing. We start with stirring rods arranged in a lattice, pairs of which execute either clockwise or counterclockwise switches. Collections of these braid generators which can be executed on the lattice simultaneously constitute a braid operator, and a time ordered set of braid operators constitutes a lattice braid. We have a novel algorithm that uses a topological characterization of material lines to find their evolution under the action of lattice braids. We are interested in what patterns of lattice braids maximize the mixing. We also explore the mixing produced through randomly chosen braids. [Preview Abstract] 
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