Bulletin of the American Physical Society
APS March Meeting 2010
Volume 55, Number 2
Monday–Friday, March 15–19, 2010; Portland, Oregon
Session V8: Spots, Stripes, and Turbulence |
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Sponsoring Units: GSNP DFD Chair: John Gibson, Georgia Institute of Technology Room: Portland Ballroom 255 |
Thursday, March 18, 2010 8:00AM - 8:36AM |
V8.00001: Turbulent-Laminar Patterns in Pipes and Channels Invited Speaker: Dwight Barkley When fluid flows through a channel, pipe, or duct, there are two basic forms of motion: smooth laminar motion and complex turbulent motion. The discontinuous transition between these states is a fundamental problem that has been studied for more than 100 years. What has received far less attention is the large-scale nature of the turbulent flows near transition once they are established. We have carried out extensive numerical computations in pipes and channels to investigate the nature of transitional turbulence in these flow. We show the existence of three fundamentally different turbulent states separated by two distinct Reynolds numbers. In the case of pipe flow for example, below $Re$ approximately 2200, turbulence takes the form of familiar equilibrium (or long-time transient) puffs. The turbulence is intensive -- puffs are localized and the ratio of turbulent to laminar flow is not dictated by system size but by factors such as initial conditions. At $Re=2200$ the flow makes a striking transition to extensive turbulence where the amount of turbulent flow scales with pipe length. The asymptotic state is an irregular (intermittent) alternation of turbulent and laminar flow whose complexity is inherent and does not result from random initial disturbances. Intermittency continues until $Re=2500$ where the intermittency factor, and other measures, reveal a continuous transition to a state of uniform turbulence along the pipe. We argue that these states are a manifestation of universal large-scale structures in transitional shear flows. [Preview Abstract] |
Thursday, March 18, 2010 8:36AM - 9:12AM |
V8.00002: Laboratory measurements of Exact Coherent Structures in 2D and 3D Turbulence Invited Speaker: Michael Schatz Recent theoretical advances suggest ways to find unstable exact Navier Stokes solutions that capture many features of coherent structures, which have long been observed in turbulent flow. At present, it remains unknown whether these solutions, termed Exact Coherent Structures, can describe observations of turbulent flow in laboratory experiments. We describe experimental measurements of Exact Coherent Structures in two settings: (1) quasi-2D flows driven by electromagnetic forces and (2) shear-driven turbulence in circular Couette flow. In both cases, time series of velocity fields are obtained from images of the visualized flow. Analysis of velocity field data provides evidence for the existence of Exact Coherent Structures in the form of unstable fixed points and periodic orbits. [Preview Abstract] |
Thursday, March 18, 2010 9:12AM - 9:48AM |
V8.00003: Homoclinic Snaking in Simple PDE Systems Invited Speaker: John Burke Spatially localized structures occur in many systems of physical interest, and are often organized in a so-called ``snakes-and-ladders'' structure. In simple PDE systems this is a consequence of a related phenomena called homoclinic snaking. In recent years the Swift-Hohenberg equation has garnered much attention as the canonical model exhibiting this behavior. In this talk I will review the standard features of homoclinic snaking in the Swift-Hohenberg equation, and also discuss the generalization of these results to other simple PDE systems. [Preview Abstract] |
Thursday, March 18, 2010 9:48AM - 10:24AM |
V8.00004: Localized states in convective systems Invited Speaker: Edgar Knobloch Many fluid systems exhibit spatially localized structures in response to spatially homogeneous forcing. Such structures are examples of dissipative solitons and in convective systems are called convectons. This talk will focus on the origin and properties of convectons in binary fluid convection [1], i.e., a mixture of two miscible components heated uniformly from below. In this system the convectons come in two types, with odd and even parity. The convectons are located in parameter space in a region called the pinning region and are organized in the so-called snakes-and-ladders structure of this region [2]. This region also contains a variety of hole-like states as well as bound states of two or more convectons. The talk will describe this structure on large periodic domains and its modification in finite domains due to the suppression of concentration pumping across odd parity convectons [3]. The geometry responsible for this rich behavior implies applicability of the results to a wide variety of physical systems, including natural doubly diffusive convection, surface tension driven convection and shear flow instability, in addition to other pattern-forming systems. \newline [1] O. Batiste, E. Knobloch, A. Alonso, and I. Mercader, J. Fluid Mech. 560, 149 (2006) \newline [2] J. Burke and E. Knobloch, Chaos 17, 037102 (2007) \newline [3] I. Mercader, O. Batiste, A. Alonso and E. Knobloch, Phys. Rev. E 80, 025201(R) (2009) [Preview Abstract] |
Thursday, March 18, 2010 10:24AM - 11:00AM |
V8.00005: Localization and homoclinic snaking in plane Couette flow Invited Speaker: Tobias M. Schneider For linearly stable shear flows such as pipe and plane Couette flow exact equilibrium and traveling wave solutions of the Navier-Stokes equations have recently been shown to play key roles in the transition to turbulence and the turbulent dynamics itself. Until now such solutions have been computed only for small, spatially periodic domains. Here we examine a new class of spatially localized solutions to plane Couette flow. Under continuation in Reynolds number these solutions exhibit a sequence of saddle-node bifurcations strikingly similar to the ``homoclinic snaking'' phenomenon observed in the Swift-Hohenberg equation. The localized solutions originate from bifurcations off the spatially periodic equilibria discovered by Nagata and others and retain their physical structure, demonstrating the relevance of exact solutions to turbulent flows in spatially extended domains, where localized perturbations are observed to induce spatially localized patches of turbulence which slowly invade the surrounding laminar flow. [Preview Abstract] |
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