Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session H10: Instability: Jets, Wakes and Shear Layers V |
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Chair: Tobias Schneider, Max Planck Institute for Dynamics and Self-Organization Room: 25C |
Monday, November 19, 2012 10:30AM - 10:43AM |
H10.00001: Local and global states in a reduced model for shear flows Matthew Chantry, Rich Kerswell A large body of work in shear flow turbulence has involved finding fixed point, travelling wave or periodic orbits, whose manifolds shape the phase space of turbulence. Most of the solutions found fill their periodic domains and are therefore not helpful in understanding localized turbulence. Recent work has pointed to connections between these spatially periodic solutions and versions of these solutions localized in at least one spatial dimension. In this work we consider a nine mode PDE model for shear flow turbulence, which depends on one spatial direction, and attempt to understand this connection between localized and periodic solutions. [Preview Abstract] |
Monday, November 19, 2012 10:43AM - 10:56AM |
H10.00002: Sensitivity analysis of the periodic orbits of plane Couette flow Onofrio Semeraro, Flavio Giannetti, Luca Brandt In the last decade, concepts from dynamical systems have been applied to gain insight onto transition to turbulence in shear flows, such as pipe and plane Couette flow. For the latter, several nontrivial equilibrium solutions, travelling waves and periodic orbits were found, enabling the analysis of transition from a new perspective. In this contribution, we study the sensitivity of unstable periodic orbits in Couette flow. These limit cycles are dominated by the self-sustained interaction between vortices and streaks. By applying the Floquet analysis, we calculate the flow Lyapunov exponent; investigating the most unstable Floquet modes and the related adjoint modes, we analyze the eigenvalue sensitivity to localized structural perturbations over the orbit period. Preliminary results confirm that the core of the instability coincides with the region where the streaks are bent, in agreement with previous numerical results. In the final contribution the analysis will be completed by considering the sensitivity of the limit-cycle frequency and amplitude to feedback forcing. [Preview Abstract] |
Monday, November 19, 2012 10:56AM - 11:09AM |
H10.00003: The edge in models of shear flows Norman Lebovitz, Giulio Mariotti A characteristic feature of the onset of turbulence in shear flows is the appearance of an ``edge,'' a codimension-one invariant manifold that separates orbits that decay rapidly to the laminar state from orbits that decay more slowly. We investigate its structure by considering a series of models of successively higher dimension. We hope in this way to isolate geometric features that are robust under the increase of dimension and are therefore candidates for extrapolation to arbitrarily high dimension. We find in the cases considered that there are extensive ranges of the Reynolds number in which all or part of the boundary of the basin of attraction of the laminar state indeed has the character of an edge. The edge is also the stable manifold of an edge state (a ``lower-branch'' state). An important feature of the edge is that it lies in a region of phase space which, while unbounded in some directions, is bounded in others. This allows orbits on either side of it to connect to the laminar state. The boundedness of the edge is associated with the presence of a further invariant (``upper-branch'') state. [Preview Abstract] |
Monday, November 19, 2012 11:09AM - 11:22AM |
H10.00004: Infinity-norm optimal perturbations in 2D plane Poiseuille flow Dimitry P.G. Foures, Colm-Cille P. Caulfield, Peter J. Schmid Since the emergence of the concept of non-modal stability analysis in the early 90's, many efforts have been made in order to identify the optimal linear mechanisms at stake in the finite-time triggering of highly energetic perturbations in a linearly stable flow. The objective functional typically involved an integrated measure of the total perturbation KE over the domain. In some circumstances however, one may be interested in identifying perturbations which lead to a maximum localized peak value of KE. This problem requires a departure from maximization of the usual quadratic norm (an inherently global measure) of the velocity field. As a demonstration case, we choose to investigate $\infty$-norm optimal perturbations in a 2D plane Poiseuille flow at $Re = 4000$. We show that for any optimization time horizon, two branches of solutions exist, either associated with perturbations localized in the centre of the domain (``centre mode'') or close to the domain boundaries (``wall mode''). We find that for $T\la 0.5T_O$ and $T\ga 2T_O$ (with $T_O$ the global optimal time for total KE), the wall modes are more efficient at producing highly energetic localized perturbations, while centre modes are optimal for intermediate times $0.5T_O\la T\la 2T_O$ only. [Preview Abstract] |
Monday, November 19, 2012 11:22AM - 11:35AM |
H10.00005: Localization in shear flow turbulence Tobias M. Schneider, John F. Gibson, John Burke Transitional turbulence in shear flows such as Couette flow is often characterized by spatio-temporal patterns and the coexistence of laminar and turbulent flow. Some of those spatial features are captured by new classes of spatially localized exact coherent structures. They are related to their known periodic counterparts and some show bifurcation structures very similar to those observed in simpler pattern-forming systems. Characterizing those solutions and generalizing the dynamical systems view of turbulence to capture the full spatio-temporal dynamics is a step towards developing a general theory of patterns in shear flows. [Preview Abstract] |
Monday, November 19, 2012 11:35AM - 11:48AM |
H10.00006: New exact coherent states in plane Poiseuille flow Masato Nagata, Kengo Deguchi Two new classes of traveling wave solution are found in plane Poiseuille flow by continuing the stationary and traveling hairpin vortex states in plane Couette flow. One of them, referred to as MS hereafter, arises from a saddle-node bifurcation, characterized by two planes of mirror-symmetry perpendicular to the span-wise direction. The second new class solution, referred to as AS hereafter, bifurcates by breaking the mid-plane symmetry of the first class. Both MS and AS are characterized by two quasi-stream-wise low-speed streaks within one span-wise period. The low-speed streaks are aligned with the vertical planes of mirror symmetry, with their width varying in a varicose fashion in the stream-wise direction. These streaks appear close to both top and bottom channel walls for MS, and to only one of the channel walls for AS. We find that the Reynolds numbers at the saddle-node bifurcation for MS and AS are smaller than that of the exact coherent state in plane Poiseuille flow known to date found by Waleffe (2003). [Preview Abstract] |
Monday, November 19, 2012 11:48AM - 12:01PM |
H10.00007: Phase transition to sustained turbulence in pipe flow Mukund Vasudevan, Marco Vassallo, Bjorn Hof Turbulence in pipe flow can first arise at Reynolds numbers somewhat below 2000. Here turbulent structures (``puffs'') are localized and have a finite lifetime. Turbulence can also proliferate through puff splitting and it has recently been proposed that turbulence overall becomes sustained when this spreading process outweighs the decay of individual structures. In the present study we measure the decay rate of turbulent puffs in two different set ups: In the first the pressure difference across the experiment is held fixed. In the second the flow is driven a piston system that enforces a constant flow rate. Measurements in both set ups are in excellent qualitative agreement and confirm that individual turbulent puffs are intrinsically transient and decay following a memoryless process. Exploiting the memoryless nature a pipe with quasi periodic boundary conditions is constructed allowing indefinitely long observation times of puff sequences. This method for the first time allows to directly measure the asymptotic evolution of the turbulent flow and to determine the equilibrium turbulent fraction close to the critical point. [Preview Abstract] |
Monday, November 19, 2012 12:01PM - 12:14PM |
H10.00008: Evolution of K- and H-type structures in a spatially evolving channel flow Alec Kucala, Sedat Biringen, Scott Waggy A fully parallel, direct numerical simulation (DNS) is performed on the full time-dependent, three-dimensional Navier-Stokes equations in a spatially developing plane-channel flow at $Re=10,000$, in which two-dimensional eigenfunctions based on the solution of the Orr-Sommerfeld equation are introduced at the inlet with uniform random noise $A_r<10^{-3}$ added along the spanwise and wall-normal directions. The flow is allowed to ``choose'' a path to secondary instability, K-type (after Klebanoff) or H-type (after Herbert), depending on the amplitude of the 2D disturbance. Detailed analysis of the spatial evolution of the primary, fundamental and subharmonic modes are presented to examine the path of secondary transition. Flow visualizations using Lagrangian coherent structures (LCS) are shown, giving physical insight into the coherent structures involved in the breakdown of laminar flow in a plane-channel. [Preview Abstract] |
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