Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session E8: Nonlinear Dynamics: Immersed Boundary, Wakes and Bounded Flows |
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Chair: Philipp Schlatter, KTH Royal Institute of Technology Room: B116 |
Sunday, November 20, 2016 5:37PM - 5:50PM |
E8.00001: Nonlinear Dynamics of a Spring-Supported Piston in a Vibrated Liquid-Filled Housing: I. Analysis J.R. Torczynski, T.J. O'Hern, J.R. Clausen The nonlinear dynamics of a piston supported by a spring in a vibrated liquid-filled housing is analyzed. The liquid is viscous, and the flow passages are narrow and depend on piston position. Ordinarily, the piston motion is highly damped. However, if bellows are added to both ends of the housing, then the piston, liquid, and bellows can execute a collective motion that forces relatively little liquid through the flow passages and thus has low damping and a strong resonance. At this frequency, the motion is large, and the nonlinearity from the flow passages produces a net force on the piston that can cause it to compress its spring. This nonlinear dynamical system is analyzed using a perturbation expansion of the Navier-Stokes equations, and the perturbation results are compared to corresponding ALE Navier-Stokes simulations. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. [Preview Abstract] |
Sunday, November 20, 2016 5:50PM - 6:03PM |
E8.00002: Nonlinear Dynamics of a Spring-Supported Piston in a Vibrated Liquid-Filled Housing: II. Experiments T.J. O'Hern, J.R. Torczynski, J.R. Clausen The nonlinear dynamics of a piston supported by a spring in a vibrated liquid-filled housing is investigated experimentally. The housing containing the piston and the liquid is subjected to vibrations along its axis. A post fixed to the housing penetrates a hole through the piston and produces a flow resistance that depends on piston position. Flexible bellows attached to the housing ends enable the piston, liquid, and bellows to execute a collective motion that forces little liquid through the flow resistance. The low damping of this motion leads to a resonance, at which the flow-resistance nonlinearity produces a net force on the piston that can cause it to compress its spring. Experiments are performed to investigate the nonlinear dynamics of this system, and these results are compared to theoretical and numerical results. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. [Preview Abstract] |
Sunday, November 20, 2016 6:03PM - 6:16PM |
E8.00003: Computation of the deformation spectrum for flows on a sphere Siavash Ameli, Shawn Shadden The most common example of flow on a manifold is flow on a sphere with numerous geophysical examples. In this talk we consider the direct and accurate computation of the nonlinear deformation tensor describing fluid kinematics on manifold surfaces, and in particular efficient computation on spherical domains. We demonstrate that standard spherical coordinate computations are undesirable and instead integration of the singular deformation tensor in Cartesian coordinates restricted to the sphere can be advantageous. This approach yields a set of differential algebraic equations that can be reduced by symmetry to yield differential equations for a 2D flow. We have applied our method to the steady and unsteady flows generated by vortex sets on the sphere as well as geophysical flow models. For the former, we demonstrate that the evolution equations near the vortices can become singular and numerically unstable. To resolve this, we derived an exact solution for the spectral components of the deformation tensor near the vortices, which also enables us to match and validate our numerical solution. [Preview Abstract] |
Sunday, November 20, 2016 6:16PM - 6:29PM |
E8.00004: Vortical and modal network analysis of unsteady cylinder wake Aditya Nair, Muralikrishnan Gopalakrishnan Meena, Kunihiko Taira, Steven Brunton Characterization of vortical and modal interactions among coherent structures in unsteady fluid flows is essential in understanding its complex behavior. Through a canonical example of incompressible flow over a circular cylinder at low Reynolds number, we quantify the interaction properties for both the vortical-wake and modal-interaction networks. For the vortical interactions, we represent the vortex elements as nodes and induced velocity between them as edge weights. With this formulation, we are able to capitalize upon network-theoretical toolsets to identify key vortical nodes and edges. Analogously, the modal-interaction network can be formulated using the modal decomposition bases and the coupling functions over the network. Based on this viewpoint, perturbations can then be tracked in terms of their amplitude and phase dynamics. We compare and contrast these network-based approaches to analyze unsteady fluid flows and discuss their implications in uncovering complex nonlinear dynamics and potential strategies towards flow field manipulation. [Preview Abstract] |
Sunday, November 20, 2016 6:29PM - 6:42PM |
E8.00005: Nonlinear wavetrains in viscous conduits Michelle Maiden, Mark Hoefer Viscous fluid conduits provide an ideal system for the study of dissipationless, dispersive hydrodynamics. A dense, viscous fluid serves as the background medium through which a lighter, less viscous fluid buoyantly rises. If the interior fluid is continuously injected, a deformable pipe forms. The long wave interfacial dynamics are well-described by a dispersive nonlinear partial differential equation. In this talk, experiments, numerics, and asymptotics of the viscous fluid conduit system will be presented. Structures at multiple length scales are discussed, including solitons, dispersive shock waves, and periodic waves. Modulations of periodic waves will be explored in the weakly nonlinear regime with the Nonlinear Schr\"odinger (NLS) equation. Modulational instability (stability) is identified for sufficiently short (long) periodic waves due to a change in dispersion curvature. These asymptotic results are confirmed by numerical simulations of perturbed nonlinear periodic wave solutions. Also, numerically observed are envelope bright and dark solitons well approximated by NLS. [Preview Abstract] |
Sunday, November 20, 2016 6:42PM - 6:55PM |
E8.00006: Observation of dispersive shock waves, solitons, and their interactions in viscous fluid conduits Dalton Anderson, Michelle Maiden, Nicholas Lowman, Marika Schubert, Mark Hoefer Dispersive shock waves (DSWs) and solitons are fundamental structures in dispersive hydrodynamics, but studies have been severely constrained. Here we report on a novel testbed called the conduit system where one fluid is moved through another via a fluid pipe with virtually no mass diffusion. The interfacial dynamics of this pipe are conservative and are modeled by a scalar, nonlinear, dispersive wave equation, similar to those describing a superfluid. Resultantly, the interfacial waves are effectively dissipationless, which enables high fidelity observations of coherent phenomena such as large amplitude DSWs [1]. Experiments involving solitons, wavebreaking leading to DSWs, and their interactions will be presented. ~The results include the refraction and absorption of a soliton by a DSW and the refraction of a DSW by a second DSW, resulting in two-phase behavior. ~Excellent agreement between nonlinear wave averaging, numerics, and laboratory experiments will be presented. The nonlinear wave dynamics observed in this model system have implications for a broad range of other conservative dispersive hydrodynamic systems. Reference: [1] Maiden et al., PRL 116, 174501 (2016). [Preview Abstract] |
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