Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session M32: Nonlinear Dynamics V 
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Chair: Laurette S. Tuckerman, ESPCI ParisTech Room: 2020 
Tuesday, November 25, 2014 8:00AM  8:13AM 
M32.00001: Burgers Turbulence on a Fractal Fourier set Michele Buzzicotti, Luca Biferale, Uriel Frisch, Samriddhi Ray We present a systematic investigation of the effects introduced by a fractal decimation in Fourier space on stochastically forced onedimensional Burgers equations. The aim is to understand the statistical robustness of the shock singularity under different reductions of the number of the degrees of freedom. We perform a series of direct numerical simulations by using a pseudospectral code with resolution up to 16384 points and for various dimensions of the fractal set of Fourier modes D$_F$ \textless 1. We present results concerning the scaling properties of statistical measures in real space and the probability distribution functions of local and nonlocal triads in Fourier space. [Preview Abstract] 
Tuesday, November 25, 2014 8:13AM  8:26AM 
M32.00002: Neurophysiology of pipe flow Dwight Barkley This work explores the connection between the transition to turbulence in pipe flow and the dynamics of excitable media, as exemplified by nerve cells. The primary goal is to leverage years of extensive analysis of neural systems to understand the dynamics of transitional turbulence. To demonstrate the predictive nature of the approach, model simulations will be presented for puffs in pipe flow for cases not previously studied experimentally. [Preview Abstract] 
Tuesday, November 25, 2014 8:26AM  8:39AM 
M32.00003: The SelfSustaining Process for Taylorvortex flow Laurette Tuckerman, Tommy Dessup, Dwight Barkley, Jose Eduardo Wesfreid, Ashley Willis The SelfSustaining Process (SSP) of Waleffe, like Hall's VortexWave Interaction theory, was proposed as the fundamental element of turbulence in low Reynolds number turbulence in wallbounded shear flows and consists of three phases. (i) Streamwise vortices bend nd the streamwise velocity contours via advection. (ii) The undulating streamwise velocity leads to waviness in the vortices via KelvinHelmholtz instability. (iii) Nonlinear interaction of the wavy streamwise vortices promotes the streamwise vortices. We explore the SSP for Taylorvortex flow, for which streamwise (azimuthal) and wavy vortices are genuine steady states resulting from linear instabilities with welldefined thresholds. In particular, we determine the circumstances under which wavy vortices reinforce Taylor vortices. [Preview Abstract] 
Tuesday, November 25, 2014 8:39AM  8:52AM 
M32.00004: The onset of turbulence in a square duct flow Gregoire Lemoult, Bjorn Hof Wall bounded shear flows experience a sudden transition from a laminar state to turbulence as Reynolds number, $Re$, increases. K. Avila \textit{et al.} (Science 333, 2011) recently characterized the onset of turbulence in pipe flow. They measured the probability for a localized disturbance to decay or spread and defined the critical Reynolds number, $Re_{\mathrm{c}}$, where the characteristic time for both process is equal. Using the same methodology, we measure these probabilities, decay and splitting, as a function of $Re$ in a 1200 $D$ long square duct, where $D$ is the width of the duct. We found the expected exponential probability distribution for both processes which underlines their memoryless character. From the characteristic time of these distributions, we estimate the point where turbulence first becomes sustained in a square duct flow. The main difference with pipe flow is that the characteristic time at $Re_{\mathrm{c}}$ is shorter making it more suitable for measurements of critical exponents in the framework of phase transition. These results also emphasize the universal behavior of the transition to turbulence in wall bounded shear flows. [Preview Abstract] 
Tuesday, November 25, 2014 8:52AM  9:05AM 
M32.00005: Direct laminarturbulent transition in TaylorCouette flow: Experiments and simulations Christopher J. Crowley, Michael Krygier, Samuel G. Raben, Daniel Borrero, Roman O. Grigoriev, Michael F. Schatz The transition to turbulence in TaylorCouette flow is frequently mediated by stable flow states (e.g. interpenetrating spirals). We describe a direct laminarturbulent transition in a system with counterrotating cylinders and small aspect ratio of 5.26. In experiments probed using tomographic PIV and direct numerical simulations with realistic boundary conditions, we find the transition is hysteretic, yet highly reproducible with turbulence triggered by the growth of weak spiral flows. [Preview Abstract] 
Tuesday, November 25, 2014 9:05AM  9:18AM 
M32.00006: Fiber bundles and geometric phases of turbulent pipe flows Francesco Fedele In this talk, I will discuss the role of continuous translation symmetries in the dynamics of turbulent pipe flows. Drawing from differential geometry, the geometric structure of the Ndimensional state space V of the Navier Stokes pipe flow can be defined by means of a base manifold P of dimension N1 (quotient space) and 1D fibers attached to any point p of P (fiber bundle). In V, a trajectory can be observed in a special comoving frame, from which the motion is locally transversal to the fibers (horizontal transport). The proper shift along the fibers to bring the motion in the comoving frame is called dynamical phase. This is, for example, the translational shift induced by the constant speed of a traveling wave (TW), or relative fixed point. A TW in state space projects to a fixed point on the base manifold P, whereas a relative periodic orbit (RPO) reduces to a periodic orbit (PO). In this case, the shift along the fibers includes also a geometric phase, induced by curvature of the base manifold P. As an application, I will present results on symmetry reduction of experimental pipe flow data acquired by means of Laser Induced Fluorescence (LIF) techniques exploiting a generalization of Hopf fibrations and complex projective spaces. A chaotic Lorenztype dynamics is unveiled in the desymmetrized state space. Moreover, the analysis reveals that the timevarying speed of a turbulent peak during bursts is related to the geometric phase associated with the motion in the fiber bundle. [Preview Abstract] 
Tuesday, November 25, 2014 9:18AM  9:31AM 
M32.00007: StreamwiseLocalized Solutions with natural 1fold symmetry Sebastian Altmeyer, Ashley Willis, Bj\"orn Hof It has been proposed in recent years that turbulence is organized around unstable invariant solutions, which provide the building blocks of the chaotic dynamics. In direct numerical simulations of pipe flow we show that when imposing a minimal symmetry constraint (reflection in an axial plane only) the formation of turbulence can indeed be explained by dynamical systems concepts. The hypersurface separating laminar from turbulent motion, the edge of turbulence, is spanned by the stable manifolds of an exact invariant solution, a periodic orbit of a spatially localized structure. The turbulent states themselves (turbulent puffs in this case) are shown to arise in a bifurcation sequence from a related localized solution (the upper branch orbit). The rather complex bifurcation sequence involves secondary Hopf bifurcations, frequency locking and a period doubling cascade until eventually turbulent puffs arise. In addition we report preliminary results of the transition sequence for pipe flow without symmetry constraints. [Preview Abstract] 
Tuesday, November 25, 2014 9:31AM  9:44AM 
M32.00008: Kolmogorovlike Flow: Effect of the Boundaries on Stability and Transition to Weak Turbulence Ravi Kumar Pallantla, Balachandra Suri, Jeffrey Tithof, Schatz Michael, Roman Grigoriev The dynamical description of turbulence in fluid flows using nonchaotic unstable solutions of the NavierStokes equation, called Exact Coherent Structures (ECS), is a promising approach to understand and control the turbulence. However, it has never been properly validated in experiment. This talk discusses a quasitwodimensional implementation of the Kolmogorov flow that enables validation of both dynamical and statistical aspects of the ECSbased description of weak turbulence. We use a numerical model of an experiment, which employs an electromagneticallydriven thin layer of electrolyte supported by a thin layer of a liquid dielectric, to describe the effects of the boundary conditions and the system size on the stability of the base flow as well as the properties of ECS which emerge in the turbulent regime. [Preview Abstract] 
Tuesday, November 25, 2014 9:44AM  9:57AM 
M32.00009: Search for Exact Coherent Structures in a QuasiTwoDimensional KolmogorovLike Flow Balachandra Suri, Jeffrey Tithof, Ravi Kumar Pallantla, Roman Grigoriev, Schatz Michael Recent theoretical advances suggest that turbulence can be characterized using unstable solutions of the NavierStokes equations having regular temporal behavior, called Exact Coherent Structures (ECS). Due to their experimental accessibility and theoretical tractability twodimensional flows provide an ideal setting for the exploration of turbulence from a dynamical systems perspective. In our talk, we present a combined numerical and experimental study of electromagnetically driven flows in a shallow layer of electrolyte. On the numerical front we present our research concerning the search for ECS in a twodimensional Kolmogorovlike flow. We discuss the change in the dynamics of the flow as the Reynolds number is varied. For a weakly turbulent flow, we show that the turbulent trajectory explores a region of state space which contains a number of ECS, including equilibria and periodic orbit solutions. We then discuss the occurrence of states similar to these numerically computed ECS in an experimental quasitwodimensional Kolmogorovlike flow. [Preview Abstract] 

M32.00010: ABSTRACT WITHDRAWN 
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