Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session M19: Instability General I |
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Chair: Yuriko Renardy, Virginia Polytechnic Institute and State University Room: 322 |
Tuesday, November 22, 2011 8:00AM - 8:13AM |
M19.00001: Spatially localized solutions of plane Couette flow John Gibson, Evan Brand We present several new spatially localized solutions of plane Couette flow, each with finite spanwise extent and periodic streamwise structure, and with several different symmetry groups. One new solution is a localized version of the ``hairpin vortex'' solution of plane Couette flow discovered independently by Itano and Generalis (PRL 2009) and Gibson et al (JFM 2009). The new solutions notably do not exhibit the homoclinic snaking seen in the localized solutions of Schneider et. al (PRL 2010). We also show that the exponential decay rate of the tails of the localized solutions is governed by the wavenumber of the solution's streamwise periodicity. [Preview Abstract] |
Tuesday, November 22, 2011 8:13AM - 8:26AM |
M19.00002: Linear stability of inviscid free surface parallel shear flows Yuriko Renardy, Michael Renardy We study the linear stability of a class of inviscid parallel shear flows of finite depth with a free surface at the top boundary and a wall at the bottom boundary. We include gravity, but not surface tension. Sample velocity profiles include Poiseuille flow and the hyperbolic tangent shear layer. We determine stability boundaries with respect to the wavenumber of the perturbation, and the relationship of the neutral limiting modes to the velocities at the bottom, at extrema of the baseflow and at inflection points. [Preview Abstract] |
Tuesday, November 22, 2011 8:26AM - 8:39AM |
M19.00003: Velocities of laminar-turbulent fronts in plane Couette flow Yohann Duguet, Philipp Schlatter, Dan Henningson We investigate numerically the motion of the fronts separating laminar from turbulent zones in subcritical shear flows, with an emphasis on localised turbulent spots in plane Couette flow. A data-driven stochastic analysis of the simulation data is used to compute the average velocities of fronts, in the special cases where they are constrained to travel either in the spanwise or streamwise direction, as the Reynolds number \textit{Re} varies. A quantitative comparison is performed with data for the front velocities of unconstrained spots (from large domain computations). It reveals the dynamical role of a large-scale, nearly two-dimensional secondary flow, which accelerates the front in the spanwise direction and deccelerates it in the streamwise direction. An extrapolation of the underlying linear advection mechanism to the lowest-transitional values of \textit{Re} explains some of the self-organisation properties of laminar-turbulent patterns in the intermittent regime. [Preview Abstract] |
Tuesday, November 22, 2011 8:39AM - 8:52AM |
M19.00004: Experiments on the onset of turbulence in shear flows Kerstin Avila, Bj\"orn Hof The onset of turbulence in pipe flow occurs via competition of two contrary processes, relaminarization and spreading of turbulence. The timescales of these processes are balanced at Reynolds number $Re = 2040 \pm 10$ and set the onset of sustained turbulence in pipe flow [1]. However, the extremely long timescales of these processes in pipe flow make it impossible to measure important signatures of criticality, such as the scaling of turbulent fraction. This information would be helpful in determining the phase transition class of the onset of turbulence in shear flows. With this goal in mind we have built a Taylor-Couette experiment with an aspect ratio of more than 200 and an azimuthal length of more than 300 gap-widths, allowing us to measure turbulent fractions in the vicinity of the critical point. We also analyze the primary stability of the flow in the counter-rotating regime and present lifetime measurements. \\[4pt] [1] K. Avila, D. Moxey, A. De Lozar, M. Avila, D. Barkley, B. Hof, Science 333(6039), 192-196, 2011 [Preview Abstract] |
Tuesday, November 22, 2011 8:52AM - 9:05AM |
M19.00005: Simple models for shear flow transition Dwight Barkley I will discuss recent developments in modeling transitional shear flows with simple two-variable models. Both pipe flow and plane Couette flow are considered. The essential insight is that most large-scale features of these shear flows can be traced to a change from excitability to bistability in the local dynamics. Models are presented in two variables, turbulence intensity and mean shear. A PDE model of pipe flow captures the essence of the puff-slug transition as a change from excitability to bistability. Extended models with turbulence as deterministic transient chaos or multiplicative noise reproduce almost all large-scale features of transitional pipe flow. In particular they capture metastable localized puffs, puff splitting, slugs, localized edge states, a continuous transition to sustained turbulence via spatiotemporal intermittency (directed percolation), and a subsequent increase in turbulence fraction towards uniform, featureless turbulence. A model that additionally takes into account the symmetries of plane Couette flow reproduces localized turbulence and periodic turbulent-laminar bands. [Preview Abstract] |
Tuesday, November 22, 2011 9:05AM - 9:18AM |
M19.00006: Spatio-temporal dynamics in transitional shear flows Bruno Eckhardt, Korinna Allhoff The spatio-temporal dynamics of transition pipe flow is dominated by the interplay between a local decay of turbulent puffs and the spreading of turbulence to neighboring regions. Much of the dynamics can be captured by a cellular model with two parameters that describe the local persistence and the spreading. The model shows a transition from a transient turbulence to a persistent one for sufficiently strong spreading. The bulk properties of the model fall into the universality class of 1+1-d directed percolation. The model can also be used to analyze the dynamics of local excitations. These localized excitations show an initial phase of spreading, which is followed by a slower spreading in the parameter range of persistent turbulence, or a contraction and a decay for transient turbulence. The observations are also compared to observations on turbulent spots in plane Couette flow. [Preview Abstract] |
Tuesday, November 22, 2011 9:18AM - 9:31AM |
M19.00007: Wake evolution and trailing vortex instabilities Ylva Odemark, Jens H.M. Fransson The production losses and inhomogeneous loads of wind power turbines placed in the wake of another turbine is a well-known problem when building new wind power farms, and a subject of intensive research. The present work aims at developing an increased understanding of the behaviour of turbine wakes, with special regard to wake evolution and the stability of the trailing vortices. Single point velocity measurements with hot-wire anemometry were performed in the wake of a small-scale model turbine. The model was placed in the middle of the wind tunnel test section, outside the boundary layers from the wind tunnel walls. In order to study the stability of the wake and the trailing vortices, a disturbance was introduced at the end of the nacelle. This was accomplished through two orifices perpendicular to the main flow, which were connected to a high-pressure tank and two fast-switching valves. Both varicose and sinusoidal modes of different frequencies could be triggered. By also triggering the measurements on the blade passage, the meandering of the wake and the disturbance frequency, phase averaged results could be computed. The results for different frequencies as well as studies of wake evolution will be presented. [Preview Abstract] |
Tuesday, November 22, 2011 9:31AM - 9:44AM |
M19.00008: The local and global stability of confined planar wakes at Re = 100 Matthew Juniper, Outi Tammisola, Fredrik Lundell At high Reynolds numbers, wake flows become more unstable when they are confined between two flat plates. At Reynolds numbers around 100, however, global stability analyses suggest that such flows become more stable when confined, while local stability analyses suggest that they become more unstable. In this theoretical and numerical study, we combine global and local stability analyses of planar wake flows at Re = 100 to resolve this apparent contradiction. We find that confinement acts in three ways: it modifies the length of the recirculation zone if one exists, it brings the boundary layers closer to the shear layers, and it can make the flow more locally absolutely unstable. In wake flows at Re = 100 with free slip boundaries, the first and third effects work together to make the flow more unstable. In wake flows at Re = 100 with no slip boundaries, the first two effects work against the third to make the flow more stable. By combining local and global analyses, we have been able to isolate these three effects and resolve the apparent contradictions in previous work. [Preview Abstract] |
Tuesday, November 22, 2011 9:44AM - 9:57AM |
M19.00009: Instabilities in the Wake of a Thin Disk with Differents Aspect Ratio Tomasz Bobinski, Sophie Goujon-Durand, Tristan Cambonie, Jose Eduardo Wesfreid Flow past a disk was investigated experimentally in a water channel. Systematic experiments with flow visualisation and PIV measurements are presented in order to characterize the flow instabilities. As an extention of previous work, we present results of investigations on disks with different aspect ratio (diameter/thickness) varying from 1 to 24, in the range of the Reynolds numbers from 50 to 500, where stationary and oscillatory instability appear. It is presented the influence of the disk aspect ratio on the evolution of perturbations, the corresponding value of onset instability and the bifurcation branches on the instability. On basis of obtained in PIV measurements vorticity fields it was performed modal analysis. We present results of 3 dimensional, 3 components velocimetry showing detailed information about the physical mechanism of hairpin generation and compare with results in the case of instabilities behind a sphere. [Preview Abstract] |
Tuesday, November 22, 2011 9:57AM - 10:10AM |
M19.00010: Dynamical study of the three dimensional Saffman-Taylor problem Matteo Nicoli, Herv\'e Henry, Mathis Plapp The mathematical generalization of the Saffman-Taylor problem to three spatial dimensions is straightforward but, nevertheless, it has not been widely studied. Recently, Levine and Tu [Phys. Rev. A {\bf 45}, 1044 (1992)] solved numerically the problem in the axisymmetric tube geometry finding several solution branches which merge for positive values of the rescaled surface tension parameter $\bar{\gamma}$ (of the order of $10^{-3}$). Unlike the two dimensional case, it seems that for this geometry does not exists any axisymmetric solution below this threshold. We have developed a phase-field model of two viscous flows to investigate the dynamics of the 3D Saffman-Taylor problem in the regime of small $\bar{\gamma}$. Full three dimensional simulations in a channel with square section and two dimensional axisymmetric simulations in the tube geometry show that the growing finger undergoes a Plateau-Rayleigh instability leading to pinch-off at the finger tail. Through the linear stability analysis of the tube solution in the axisymmetric geometry, we show that the solutions found by Levine and Tu are unstable for any value of $\bar{\gamma}$. Our phase-field model reproduces accurately this linear prediction and allows to study the influence of the finger tip on the pinch-off velocity. Moreover, we observe that the interface between the two fluids undergoes a tip splitting instability for $\bar{\gamma}< 6.5 \times 10^{-3}$, spoiling the stability of the Saffman-Taylor finger. [Preview Abstract] |
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