Bulletin of the American Physical Society
63rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 55, Number 16
Sunday–Tuesday, November 21–23, 2010; Long Beach, California
Session GZ: Instability: General I |
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Chair: Tobias M. Schneider, Harvard University Room: Hyatt Regency Long Beach Regency F |
Monday, November 22, 2010 8:00AM - 8:13AM |
GZ.00001: Onset of sustained turbulence in pipe flow Kerstin Avila, Alberto de Lozar, Bjoern Hof The onset of turbulence in pipe flow was first investigated by Reynolds more than 125 years ago. The laminar Poiseuille profile is linearly stable, so that the precise Reynolds number at which the flow becomes turbulent depends on the care taken to minimize disturbances in the experimental setup. In order to avoid this setup effects, an external localized perturbation is induced in the laminar flow and the development of the ensuing localized turbulent patch (puff) while traveling downstream is studied. Although it was recently found that the puffs are transient for all Re, puffs may grow and split, leading to a spread of turbulence. Here we analyze the splitting of puffs quantitatively and show that it is the competition between decaying and splitting that determines the onset of sustained turbulence. In an in depth experimental investigation, of more than 100.000 measurements in pipes of up to 3.400 diameters in length, we determine the critical Reynolds number for the onset of sustained turbulence in pipe flow. [Preview Abstract] |
Monday, November 22, 2010 8:13AM - 8:26AM |
GZ.00002: Towards uniformly turbulent pipe flow? Marc Avila, Bjoern Hof Turbulence occurs first in pipes in the form of localized spots of fluctuating but well defined size. These spots may relaminarize, merge or split, giving rise to the large-scale laminar-turbulent patterns of the transitional regime. We report on direct numerical simulations and experiments of the transition between these intermittent flows and uniform turbulence. Here, long periodic pipes of up to 500 diameters are used in order to capture the patterns selected by the flow. A large number of simulations is carried out to statistically demonstrate that the limit of uniform turbulence is only reached asymptotically. In particular, it is shown that the relaminarization probabilities of pipe sections of arbitrary lengths are nonzero. [Preview Abstract] |
Monday, November 22, 2010 8:26AM - 8:39AM |
GZ.00003: Edge formation in low-dimensional models of shear transition Norman Lebovitz Low dimensional models are used to illustrate the nature of an edge state. In these models the edge is the stable manifold of a lower-branch equilibrium point. It comes into existence in connection with the birth of a periodic orbit via a homoclinic bifurcation as a parameter (the Reynolds number) increases beyond a critical value. Even for values of the Reynolds number less than this critical value, the structure of the basin boundary is such that edge-like behavior occurs in parts of phase space. It is possible to manufacture dynamical systems for which the edge state disappears for sufficiently large parameter values. [Preview Abstract] |
Monday, November 22, 2010 8:39AM - 8:52AM |
GZ.00004: Spatially localized solutions of plane Couette flow John Gibson, Tobias Schneider, John Burke We examine spatially localized solutions of plane Couette flow: traveling waves and equilibria with finite spanwise extent and periodic streamwise structure. We show that these solutions exist over a wide range of Reynolds numbers, from Re=170 to at least Re=4000, and demonstrate a relationship between the streamwise periodicity of a solution and the range of Reynolds number over which it appears. Some solutions display a diagonal or winding symmetry, suggestively similar to the diagonal bands of structure observed in large-scale simulations by Tuckermann and Barkley. [Preview Abstract] |
Monday, November 22, 2010 8:52AM - 9:05AM |
GZ.00005: A Search for Exact Coherent Structures in Transitional Taylor-Coutte Flow Daniel Borrero-Echeverry, Donald R. Webster, Randall Tagg, Michael F. Schatz Theoretical and numerical studies have suggested that unstable, exact solutions of the Navier-Stokes equations known as Exact Coherent Structures (ECS) may provide a foundation for a simplified dynamical description of turbulence. We use tomographic particle image velocimetry to measure the velocity field of transitional Taylor-Coutte flow (TCF). Specifically, we present spatially and temporally resolved measurements of three-component, three-dimensional velocity fields of turbulent patches that show up when TCF undergoes a subcritical transition to turbulence. This transition occurs when only the outer cylinder rotates and is different from the famous transition driven by centrifugal instabilities. TCF offers the best opportunity to make the connection with current ECS theory since it maintains some of its assumptions (streamwise periodic boundary conditions and plane Couette flow (in the small-gap limit)), but also includes realistic effects (no-slip spanwise boundary conditions). [Preview Abstract] |
Monday, November 22, 2010 9:05AM - 9:18AM |
GZ.00006: On the geometry of coexisting edge states for plane Couette flow Lina Kim, Jeff Moehlis For certain shear flows, it has recently been suggested that the codimension-1 manifolds of an exact coherent structure, called an edge state, can define the boundary which separates trajectories that directly decay to the laminar state from those that become turbulent. This boundary is referred to as the edge of chaos. For a range of aspect ratios for plane Couette flow, distinct edge states can be found using an iterative method. We explore the geometry associated with these coexisting edge states, and the relationship of the edge to the turbulent and laminar dynamics. [Preview Abstract] |
Monday, November 22, 2010 9:18AM - 9:31AM |
GZ.00007: Experimental observation of the edge state in pipe flow Alberto de Lozar, Fernando Mellibovsky, Bjoern Hof Transition to turbulence in pipe flow is subcritical and therefore laminar and turbulent flows are observed at the same Reynolds number. Recent numerical studies have identified the hyper-surface in phase space which divides trajectories leading to laminar or turbulent state. Surprisingly, a single chaotic attractor (called edge state) controls the flow dynamics on this hyper-surface. It has been suggested that edge state may play an important role for transition to turbulence but up to now there is no experimental evidence to support this claim. Our goal is to look for possible signatures of edge dynamics in decaying turbulence. In a recent paper we demonstrated that turbulence at low Reynolds can be forced to decay. In our experiments we study the flow in this decaying section using two stereo PIV systems enabling us to measure velocities in two planes separated by 6 diameters. We correlate the experimentally measured velocity fields with the numerically calculated edge state. Surprisingly the experiment closely resemble the edge state for $17\%$ of the time. Additionally, the phase velocity in the experiment closely matches the traveling wave solution underlying the edge state. [Preview Abstract] |
Monday, November 22, 2010 9:31AM - 9:44AM |
GZ.00008: Eckhaus instability and homoclinic snaking in plane Couette flow John Burke, John Gibson, Tobias Schneider Homoclinic snaking in wide plane Couette channels gives rise to exact solutions of the Navier-Stokes equation which are spatially localized. In this talk, we examine the upper limit of the snaking branches, where the localized states resemble holes of laminar flow embedded in an otherwise regular spatially periodic state. The termination of the snaking branches is related to the Eckhaus instability of the spatially periodic equilibria, but also depends sensitively on the width of the domain. [Preview Abstract] |
Monday, November 22, 2010 9:44AM - 9:57AM |
GZ.00009: ABSTRACT WITHDRAWN |
Monday, November 22, 2010 9:57AM - 10:10AM |
GZ.00010: A homoclinic tangle at the edge of shear turbulence Lennaert van Veen, Genta Kawahara Experiments, simulations and theoretical arguments lend mounting evidence for the ``edge state'' hypothesis on subcritical transition to shear turbulence. The hypothesis asserts that certain states of fluid motion, such as travelling waves and time-periodic flows, mediate between laminar and turbulent motion. Locally, the stable manifold of an edge state separates laminarizing from bursting flows. The global structure of the separatrix, however, is unknown. In this presentation, we show the existence of a flow homoclinic to a time-periodic edge state in plane Couette turbulence. Through classical theorems of dynamical systems theory, this implies a complex global geometry of the separating manifold. In particular, we can expect that any turbulent flow is close to the boundary, and small perturbations can cause it to relaminarize. Also, the homoclinic flow give a preferred route from near-laminar to turbulent flow and back. We study the physical characteristics of this cycle in detail. [Preview Abstract] |
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