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 Q1: Nonlinear Dynamics: ChaosNonlinear

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Chair: Phanindra Tallapragada, Clemson University Room: 401 
Tuesday, November 21, 2017 12:50PM  1:03PM 
Q1.00001: Sensitivity analysis of hydrodynamic chaos in combustion using NILSSAD Nisha Chandramoorthy, Qiqi Wang, Luca Magri, Sri Hari Krishna Narayanan, Paul Hovland NonIntrusive Least Squares Shadowing (NILSS) is a promising new approach to compute derivatives of statistically stationary quantities of interest with respect to input parameters in chaotic dynamical systems. NILSS has recently been shown to produce accurate sensitivities in some chaotic fluid flows where conventional adjoint/tangent equationbased sensitivity computa tion fails. In this work, we introduce automatic differentiation into the NILSS algorithm, to develop the NILSSAD package. Numerical results using NILSSAD are presented for a chaotic Rijke tube model of gas turbine combustion. The lowdimensional thermoacoustic model can be tuned to produce the hydrodynamical chaotic features of the complex combustion process and gives useful sensitivities with NILSSAD. [Preview Abstract] 
Tuesday, November 21, 2017 1:03PM  1:16PM 
Q1.00002: Chaotic dynamics of a buoyancyinduced turbulent fire Kazushi Takagi, Hiroshi Gotoda, Isao Tokuda, Takaya Miyano We carry out a numerical study on the dynamic behavior of a buoyancyinduced turbulent fire from the viewpoints of symbolic dynamics and statistical complexity. The permutation entropy enables us to capture the significant changes in the dynamic behavior of flow velocity fluctuations. The possible existence of two important dynamics: lowdimensional chaos in the nearfield dominated by the motion of largescale vortices and highdimensional chaos in the farfield forming a welldeveloped turbulent plume, is clearly identified by the multiscale complexityentropy causality plane (Zunnio et al., Phys. Rev. E 86, 046210 (2012); H. Gotoda et al., Phys. Rev. E 95, 022201 (2017)). [Preview Abstract] 
Tuesday, November 21, 2017 1:16PM  1:29PM 
Q1.00003: Transition to chaos in an acoustic stirring cavity flow Gaby Launay, Tristan Cambonie, Daniel Henry, Alban Potherat, Valery Botton Acoustic streaming, as a nonintrusive flow generation method, could be a simple and efficient way of including and controlling mixing in liquid phase processes. We are for instance interested in the purification of photovoltaic silicon by directional solidification. This promising process however necessitates efficient mixing of liquid silicium in high temperature furnaces with only poor accessibility to the melt. The fundamental understanding of transition to chaos in this type of flows is a first step towards a thorough mastery of acoustic stirring. Previous experimental measurements of a cavity flow driven by four acoustic streaming jets have shown a complex dynamical transition with increasing acoustic forcing. We propose here to characterize this transition on numerical computations of this same flow by using nonlinear dynamics tools. The flow dynamics shows indeed two successive transitions to chaos, separated by a sudden simplification of the dynamics. Both those transitions are characterized using nonlinear invariants and are shown to exhibit the classical mechanisms of transition to chaos, namely Hopf bifurcations, period doubling and intermittencies. The sudden intermediate simplification of the dynamics is linked to the breaking of the vertical symmetry. [Preview Abstract] 
Tuesday, November 21, 2017 1:29PM  1:42PM 
Q1.00004: Resonant mixing between two counterrotating cylinders Dmitri Vainchtein We investigated the role of resonance phenomena in mixing in Stokes flow between two counterrotating cylinders with parallel but offset axes. When the cylinders are rotating with constant angular velocities, the mixing is absent. However, when one of the angular velocities is changed periodically, mixing appears. We show that mixing is localized near the streamlines where the period of motion along the unperturbed streamline matches the period of modulation. We discuss the width of the mixing domain in terms of the evolution of the streamfunction that plays to role of the adiabatic invariant of the system [Preview Abstract] 
Tuesday, November 21, 2017 1:42PM  1:55PM 
Q1.00005: Mixing in flows induced by singularities Senbagaraman Sudarsanam, Phanindra Tallapragada Nonlinearity of fluid flows is the leading cause of rapid mixing at macroscopic length scales, with mixing due to viscous diffusion occurring at much smaller length and much larger time scales. Linearized viscous flows also known as stokes flow is a regime of fluid flow characterized by reversibility of the flow and negligible nonlinearity, making mixing of two fluids in this regime a challenge. However, it is now well established that the Lagrangian trajectories of stokes flow can exhibit deterministic chaos even for the simple case of two dimensional flows with periodic time dependence. We use the singularity method to model several time periodic stokes flows in bounded domains and investigate the mixing induced in these flows. We construct several mixing prototypes of flows due to Stokes flow singularities and analyze the mixing using geometric and probabilistic tools used for studying phase space transport in dynamical systems. [Preview Abstract] 
Tuesday, November 21, 2017 1:55PM  2:08PM 
Q1.00006: Period Doubling, Tripling, and Quintupling in the Breakup of a Liquid Jet Driven Transversely to Axis of Motion Salome Hussein, Stuart Bradley, Geoff Willmott The RayleighPlateau instability has been the subject of study for over a century. Many modern technologies now actively take advantage of this phenomenon, from inkjet printing to fuel injection systems. In pursuit of a precision fluid delivery system, we aimed to design a monodisperse droplet generator. One approach used a piezoelectric element to oscillate the jet transversely to the axis of motion. While at certain frequencies (approx. 1.0kHz) we observed the expected and desired jet breakup behavior, lower frequencies yielded a serpentine profile along the jet, with a node and antinode, before breaking up. In addition, within a range of driving frequencies, we observed the jet splitting into multiple discrete drop trajectories, intermittently converging back into one in between those instances, then finally entering the region where the RP instability dominated. While initially considered an undesirable aspect of the design, we will demonstrate that these regions are predictable and robust enough to offer a much finer degree of control over spray coverage  as opposed to a binary choice between the pinpoint precision of a monodisperse stream and an imprecise conventional spray. [Preview Abstract] 
Tuesday, November 21, 2017 2:08PM  2:21PM 
Q1.00007: Universality of the anomalous enstrophy dissipation at the collapse of three point vortices on EulerPoincar\'{e} models Takeshi Gotoda, Takashi Sakajo Anomalous enstrophy dissipation of incompressible flows in the inviscid limit is a significant property characterizing 2D turbulence. It indicates that the investigation of nonsmooth incompressible and inviscid flows contributes to the theoretical understanding of turbulent phenomena. In the preceding study, we have considered weak solutions to the Euler$\alpha$ equations, which is a regularized Euler equations, for pointvortex initial data and shown that the evolution of three point vortices converges to a selfsimilar collapsing orbit dissipating the enstrophy at the critical time as $\alpha \rightarrow 0$. In order to elucidate whether or not this singular orbit can be constructed independently on the regularization method, we considered a functional generalization of the Euler$\alpha$ equation, called the EulerPoincar\'{e} models. We provide a sufficient condition for the existence of the singular orbit. As examples, we confirmed that the condition is satisfied with the Gaussian regularization and the vortexblob regularization. Consequently, the enstrophy dissipation via the collapse of three point vortices is a generic phenomenon that is not specific to the Euler$\alpha$ model but universal within the EulerPoincar\'{e} models. [Preview Abstract] 
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