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 A8: Nonlinear Dynamics: Coherent Structures |
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Chair: Tom Solomon, Bucknell University Room: B116 |
Sunday, November 20, 2016 8:00AM - 8:13AM |
A8.00001: Streamwise asymptotics of spatially localized solutions in plane Pouseuille flow Roman Grigoriev, Joshua Barnett Numerical advances of recent years have enabled us to find localized solutions in various canonical shear flows, for instance, relative periodic orbits in plane and pipe Poiseuille flow. These solutions have interesting properties such as the exponential decay of the leading and trailing fronts which appear to also shape the fronts of "turbulent puffs" that are found during intermittent turbulence. While arguably quite important, these exponential asymptotics are not well understood theoretically. This talk will discuss how they can be derived, or at least constrained, analytically using wave propagation theory. [Preview Abstract] |
Sunday, November 20, 2016 8:13AM - 8:26AM |
A8.00002: Hyperbolic neighborhoods as organizers of finite-time exponential stretching Sanjeeva Balasuriya, Nicholas Ouellette Hyperbolic points and their unsteady generalization, hyperbolic trajectories, drive the exponential stretching that is the hallmark of nonlinear and chaotic flow. Typical experimental and observational velocity data is unsteady and available only over a finite time interval, and in such situations hyperbolic trajectories will move around in the flow, and may lose their hyperbolicity at times. Here we introduce a way to determine their region of influence, which we term a hyperbolic neighborhood, which marks fluid elements whose dynamics are instantaneously dominated by the hyperbolic trajectory. We establish, using both theoretical arguments and numerical verification from model and experimental data, that the hyperbolic neighborhoods profoundly impact Lagrangian stretching experienced by fluid elements. In particular, we show that fluid elements traversing a flow experience exponential boosts in stretching while within these time-varying regions, that greater residence time within hyperbolic neighborhoods is directly correlated to larger Finite-Time Lyapunov Exponent (FTLE) values, and that FTLE diagnostics are reliable only when the hyperbolic neighborhoods have a geometrical structure which is regular in a specific sense. [Preview Abstract] |
Sunday, November 20, 2016 8:26AM - 8:39AM |
A8.00003: Simple computation of null-geodesics, with applications to vortex boundary detection Mattia Serra, George Haller Recent results show that boundaries of coherent vortices (elliptic coherent structures) can be computed as closed null-geodesics of appropriate Lorentzian metrics defined on the physical domain of the underlying fluid. Here we derive a new method for computing null-geodesics of general Lorentzian metrics, founded on the geometry of geodesic flows. We also derive the correct set of initial conditions for the computation of closed null-geodesics, based on simple topological properties of planar closed curves. This makes the computation of coherent vortex boundaries fully automated, simpler and more accurate compared to the existing procedure. As an illustration, we compute objective coherent vortex boundaries in Oceanic and Atmospheric Flows. [Preview Abstract] |
Sunday, November 20, 2016 8:39AM - 8:52AM |
A8.00004: Coherent structure coloring: identification of coherent structures from sparse flow trajectories using graph theory Kristy Schlueter, John Dabiri Coherent structure identification is important in many fluid dynamics applications, including transport phenomena in ocean flows and mixing and diffusion in turbulence. However, many of the techniques currently available for measuring such flows, including ocean drifter datasets and particle tracking velocimetry, only result in sparse velocity data. This is often insufficient for the use of current coherent structure detection algorithms based on analysis of the deformation gradient. Here, we present a frame-invariant method for detecting coherent structures from Lagrangian flow trajectories that can be sparse in number. The method, based on principles used in graph coloring algorithms, examines a measure of the kinematic dissimilarity of all pairs of flow trajectories, either measured experimentally, e.g. using particle tracking velocimetry; or numerically, by advecting fluid particles in the Eulerian velocity field. Coherence is assigned to groups of particles whose kinematics remain similar throughout the time interval for which trajectory data is available, regardless of their physical proximity to one another. Through the use of several analytical and experimental validation cases, this algorithm is shown to robustly detect coherent structures using significantly less flow data than is required by existing methods. [Preview Abstract] |
Sunday, November 20, 2016 8:52AM - 9:05AM |
A8.00005: Dynamically dominant exact coherent structures in turbulent Taylor-Couette flow Michael Krygier, Roman Grigoriev Unstable Exact Coherent Structures (ECS), which are solutions to the Navier-Stokes equation, provide a connection between turbulence and dynamical systems and offer a method for exploiting the low dimensionality of weakly turbulent flows. We investigate ECS in an intermittent Taylor-Couette flow (TCF) found in a small-aspect-ratio geometry with counter-rotating cylinders ($\eta=0.5$, $\Gamma=1$, $Re_i=-1200$, $Re_o=1200$). The presence of end-caps breaks the axial translational symmetry of TCF, but continuous rotational symmetry remains, which suggest that typical ECS should be the relative versions of equilibria and time-periodic orbits. Indeed, previous studies (Meseguer et al., 2009 and Deguchi, Meseguer & Mellibovsky, 2014) found several unstable traveling wave solutions (relative equilibria). We have shown that the dynamically dominant ECS for weakly turbulent TCF in the small-aspect-ratio geometry are relative periodic orbits (not relative equilibria), as evidenced by the frequent visits of their neighborhoods by the turbulent flow. [Preview Abstract] |
Sunday, November 20, 2016 9:05AM - 9:18AM |
A8.00006: Low-order invariant solutions in plane Couette flow Muhammad Ahmed, Ati Sharma Ten new equilibrium solutions of the Navier-Stokes equations in plane Couette flow are presented. The new solutions add to the inventory of known equilibria in plane Couette flow found by Nagata JFM 1990, Gibson JFM 2008, 2009, and Halcrow JFM 2008, who together found 13. These new solutions elucidate the low-dimensional nature of exact coherent structures, which are essential to defining simplified mechanisms that explain the self-sustaining nature of wall-bounded flows. In particular, one of the solutions found has a one-dimensional unstable manifold in the symmetry-invariant subspace and otherwise, like the lower branch equilibrium solution found by Nagata JFM 1990. A new method for generating initial guesses for Newton-Krylov-hookstep (NKH) searches is also presented. This method allows the NKH algorithm to find equilibrium solutions that are derived from previous solutions. [Preview Abstract] |
Sunday, November 20, 2016 9:18AM - 9:31AM |
A8.00007: Burning invariant manifolds and reaction front barriers in three-dimensional vortex flows JJ Simons, Minh Doan, Kevin Mitchell, Tom Solomon We describe experiments on the effects of three-dimensional fluid advection on the motion of the excitable, Ruthenium-catalyzed Belousov-Zhabotinsky chemical reaction. The flow is a superposition of horizontal and vertical vortices produced by magnetohydrodynamic forcing and measured with particle image velocimetry. We visualize the propagating fronts in three dimensions with a scanning, laser-induced fluorescence technique that benefits from the fluorescence of the reduced Ru indicator. The experiments reveal a combination of tube- and sheet-like barriers that block the propagating reaction fronts. We study the dependence of the structure of these barriers on the front propagation speed (normalized by a characteristic flow velocity). The locations and blocking properties of these barriers are interpreted with a six-dimensional {\it burning invariant manifold}\footnote{J. Mahoney, D. Bargteil, M. Kingsbury, K. Mitchell and T. Solomon, Europhys. Lett. {\bf 98}, 44005 (2012).} theory that follows the evolution of front elements in the flow. [Preview Abstract] |
Sunday, November 20, 2016 9:31AM - 9:44AM |
A8.00008: Equilibria and Travelling wave solutions for Couette and channel flows with longitudinal grooves Sabarish Vadarevu, Ati Sharma, Bharathram Ganapathisubramani Several classes of exact solutions for canonical flows have been computed by earlier researchers. These solutions are known to inform the flow of turbulence in state-space. We extend two classes of exact solutions, equilibria and travelling wave solutions, from flat-walled Couette and channel flows to grooved geometries with groove-amplitudes as high as 20\% of channel half-height. These solutions provide insight into the mechanics of how a wavy wall could influence turbulent flow. Plotting scalars such as the average shear stress at the wall and the bulk velocity (for channel flows) allows us to identify branches of solutions that could have greater contributions to turbulence, and reconcile the curious phenomenon of drag reduction observed in some riblet-mounted boundary layer flows. Earlier researchers have proposed using modified boundary conditions (imposed on flat surfaces) as a substitute to imposing the traditional no-slip and impermeability conditions on a rough wall. We compare solutions for grooved flows to those for flat-walled flows with modified boundary conditions to evaluate the validity of such simplification to non-laminar solutions. [Preview Abstract] |
Sunday, November 20, 2016 9:44AM - 9:57AM |
A8.00009: The orientation field of fibers advected by a two-dimensional chaotic flow Bardia Hejazi, Bernhard Mehlig, Greg Voth We examine the orientation of slender fibers advected by a 2D chaotic flow. The orientation field of these fibers show fascinating structures called scar lines, where they rotate by $\pi$ over short distances. We use the standard map as a convenient model to represent a time-periodic 2D incompressible fluid flow. To understand the fiber orientation field, we consider the stretching field, given by the eigenvalues and eigenvectors of the Cauchy-Green strain tensors. The eigenvector field is strongly aligned with the fibers over almost the entire field, but develops topological singularities at certain points which do not exist in the advected fiber field. The singularities are points that have experienced zero stretching, and the number of such points increases rapidly with time. A key feature of both the fiber orientation and the eigenvector field are the scar lines. We show that certain scar lines form from fluid elements that are initially stretched in one direction and then stretched in an orthogonal direction to cancel the initial stretching. The scar lines that satisfy this condition contain the singularities of the eigenvector field. These scar lines highlight the major differences between the passive director field and the much more widely studied passive scalar field. [Preview Abstract] |
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