Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session P07: Non-Linear Dynamics and Chaos II |
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Chair: Peko Hosoi, MIT Room: 211 |
Monday, November 25, 2019 5:16PM - 5:29PM |
P07.00001: Passive and active mixing in vortex chain flows Tom Solomon In 1988\footnote{T.H. Solomon and J.P. Gollub, Phys. Rev. A {\bf 38}, 6280-6286 (1988)}, Jerry Gollub and I published an article that first identified chaotic mixing in an oscillating chain of alternating vortices, a model developed to describe transport in time-dependent Rayleigh- B\'enard convection. In the thirty years since, the vortex chain flow (and the similar double-gyre flow) have become paradigm flows for studying fluid mixing in closed flows. In this talk, I'll review studies that have demonstrated both enhanced diffusion and superdiffusion in this system, as well as extensions to vortex arrays and three-dimensional, time-independent flows, which also show chaotic mixing. We will also discuss recent studies of active mixing -- both of propagating reaction fronts and of swimming microbes -- in vortex chain flows. [Preview Abstract] |
Monday, November 25, 2019 5:29PM - 5:42PM |
P07.00002: Particle-scale fluctuations and hindered settling of a granular dispersion at low-Re Ted Brzinski, James Stadler, Ivan Tseytlin, Charles Walker Dense dispersions of grains sedimenting in a fluid at low-Re are characterized by mean settling velocities which are hindered relative to Stokes settling. Hindered settling data can be collapsed to a master curve which is well-described by the Richardson-Zaki function $H\left(\phi\right)\equiv{v}/v_{s}=\left(1-\phi\right)^n$, where $\phi$ is the particle volume fraction, but with different exponents: $n\approx5.5$ for systems with a small Peclet number, and $n\approx4.5$ for systems with large Peclet number. This branching occurs at a surprisingly large value of Pe$\approx10^8$. We report the results of our latest experimental investigations into this unexpected behavior. Using diffusing-wave spectroscopy, we characterize the spatio-temporal particle velocity fluctuations on scales as small as the expected Brownian motion for our experimental systems, and systematically vary Peclet number around the branching-value to identify differences in the grain-scale dynamics between systems on either branch of the hindered settling function. [Preview Abstract] |
Monday, November 25, 2019 5:42PM - 5:55PM |
P07.00003: Random Organization: A Gift that Keeps on Giving David Pine, Sanuel Wilkin, Paul Chaikin Non-Brownian suspensions of spheres periodically sheared at low Reynolds number explore new configurations through collisions in an otherwise reversible flow. Below a critical strain, the particles remain active until they find a configuration with no collisions and fall into an absorbing state. Simulations by Hexner \& Levine show that the system becomes hyperuniform near the critical strain as long length-scale density fluctuations are suppressed. Using a compact rotational shear cell, we explore the effect of collision-induced diffusion on the evolution of the structure factor $S(q)$ using a confocal microscope. From dynamical measurements, we see that the effective diffusion constant is equal to the self-diffusion of the particles below the transition and increases linearly with strain amplitude above. For a 40\% volume fraction suspension, we see low-$q$ long-wavelength fluctuations suppressed near the critical strain of $\gamma=0.9$ with as $S(q)$ exhibits hyperuniform scaling. At short length scales, the nearest neighbor correlations ($S(q\approx 2\pi/a)$) reach a peak at critical. [Preview Abstract] |
Monday, November 25, 2019 5:55PM - 6:08PM |
P07.00004: Nonlinear Dynamics in Sports Anette Hosoi In celebration of Jerry Gollubâ€™s remarkable contributions to nonlinear dynamics, I would like to discuss a few examples of complex dynamical behavior in sports. In free-flowing team sports such as soccer, basketball, and hockey, the relationships between individual athletes can give rise to collective behavior that can enhance (or diminish) the effectiveness of the team. New high-quality tracking data of professional basketball and soccer players, i.e. center of mass coordinates at 25Hz with centimetric-scale resolution, reveals signatures of player fatigue, decision-making aptitude, and other athlete traits that have historically been unquantifiable. Here we borrow concepts from the analysis of the collective motion of birds and fish, e.g. schooling and flocking, to begin to draw insights from tracking data and construct a low dimensional portrait of athlete characteristics. [Preview Abstract] |
Monday, November 25, 2019 6:08PM - 6:21PM |
P07.00005: Elastic Alfven waves in elastic turbulence Victor Steinberg, Atul Varshney Speed of sound waves in gases and liquids are governed by the compressibility of the medium. There exists another type of non-dispersive wave where the wave speed depends on stress instead of elasticity of the medium. A well-known example is the Alfven wave, which propagates through plasma permeated by a magnetic field with the speed determined by magnetic tension. An elastic analogue of Alfven waves has been predicted in a flow of dilute polymer solution where the elastic stress of the stretching polymers determines the elastic wave speed. Here we present quantitative evidence of elastic Alfven waves in elastic turbulence of a viscoelastic creeping flow between two obstacles in channel flow. The key finding in the experimental proof is a nonlinear dependence of the elastic wave speed c$_{\mathrm{el}}$ on the Weissenberg number Wi, which deviates from predictions based on a model of linear polymer elasticity. [Preview Abstract] |
Monday, November 25, 2019 6:21PM - 6:34PM |
P07.00006: Mixing in Turbulent Fluids: From Quasi Two-Dimensional Systems to Stably-Stratified Shear Flows Robert Ecke Mixing in fluids represents one of the most important roles of chaotic or turbulent flows, being responsible for, among many things, the dispersion of pollutants, the efficient mixing of fuel/gas in internal combustion engines, and the distribution of heat and salinity in the ocean. I will discuss Lagrangian and Eulerian measurements of a thin layer driven by electromagnetic forcing which is an experimental realization of two-dimensional turbulence. I will also present experimental results of fully three-dimensional stably-stratified shear flows that represent geophysical problems arising from, for example, oceanic overflows and river estuaries. The simultaneous planar velocity and density fields are determined using particle image velocimetry and planar laser-induced fluorescence. Different analysis methods for characterizing the interplay between mixing and turbulence are explored including Lagrangian methods obtained from high-resolution particle tracking, filtering (coarse-graining) applied to both systems, and comparison with traditional turbulence analysis approaches. These different analysis techniques give physical insight into the mechanisms of mixing and transport in scalar advection, both the passive and active cases. [Preview Abstract] |
Monday, November 25, 2019 6:34PM - 6:47PM |
P07.00007: Geometric phase and dimensionalityÂ reduction in locomoting living systems Jennifer Rieser, Chaohui Gong, Henry Astley, Perrin Schiebel, Ross Hatton, Howie Choset, Daniel Goldman The apparent ease with which animals move requires the coordination of their many degrees of freedom to manage and properly utilize environmental interactions. Identifying effective strategies for locomotion has proven challenging, often requiring detailed models that generalize poorly across modes of locomotion, body morphologies, and environments. We present the first biological application of a gauge-theory-based geometric framework for movement, originally proposed by Wilczek and Shapere nearly 40years ago, to describe self-deformation-driven movements through dissipative environments. Using granular resistive force theory to model environmental forces and principal components analysis to identify a low-dimensional space of animal postures and dynamics, we show that our approach captures key features of how a variety of animals, from undulatory swimmers and slitherers to sidewinding rattlesnakes, coordinate body movements and leverage environmental interactions to generate locomotion. Our results demonstrate that this geometric approach is a powerful and general framework that enables the discovery of effective control strategies, which could be further augmented by physiologically-relevant parameters and constraints to provide a deeper understanding of locomotion in a wide variety of biological systems and environments. [Preview Abstract] |
Monday, November 25, 2019 6:47PM - 7:00PM |
P07.00008: Hysteresis Behavior of Large Scale Structure in Turbulent Rotating Plane Couette Flow Yuhan Huang, Zhenhua Xia, Minping Wan, Shiyi Chen The existence of counter rotating vortex pairs is important in rotating plane Couette flow (RPCF). Two groups of numerical simulation were conducted with rotation number, $Ro$ ($Ro=2\Omega h/U_w$, with $\Omega$ being the constant angular velocity in the spanwise direction, $h$ being half channel height and $U_w$ being half wall velocity difference), varying between 0.01 and 0.6. We found that the number of vortex pairs in a finite computation domain exhibits a hysteretic behavior as $Ro$ increases and decreases. When $Ro$ increases from 0.03 to 0.3, the number of vortex pairs is 2. When $Ro$ decreases from 0.3 to 0.03, the number of vortex pairs is 3. This phenomenon is related to multiple states in RPCF or state bifurcation. Turbulent statistics such as friction, turbulent kinetic energy also form hysteresis loops. A linear stability analysis is performed on this problem to explain the formation of the hysteresis behavior. [Preview Abstract] |
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