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 EE: Instability and Turbulence: Couette and Channel Flow |
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Chair: Morteza Khashehchi, University of Melbourne Room: Long Beach Convention Center 102C |
Sunday, November 21, 2010 4:10PM - 4:23PM |
EE.00001: Comparison of linear and nonlinear optimal perturbation transient growth in plane Couette flow S.M.E. Rabin, C.P. Caulfield, R.R. Kerswell Previous approaches to the question of transient growth have focused upon the study of linearised disturbances, with the assumption that it is the growth in the linear regime of linear optimal perturbations (LOPs) that nevertheless lead to a nonlinear regime and hence trigger the transition to turbulence. In this study we take a different approach by considering the full nonlinear problem. We look to extend the work considering pipe flow of Pringle (C. C. T. Pringle Ph.D. Bristol 2009) and use variational techniques to examine both the spatial structure and the normalised kinetic energy growth (gain) achieved by nonlinear optimal perturbations (NLOPs) in plane Couette flow. We show that in certain circumstances the gain achieved by the NLOP is significantly larger and has a noticeably different (and more complex) spatial structure from its counterpart LOP. We investigate the dependence on initial perturbation energy of the maximum predicted gain for selected Reynolds numbers and optimization times and propose that these inherently nonlinear structures may well be more significant in the transition to turbulence than LOPs. [Preview Abstract] |
Sunday, November 21, 2010 4:23PM - 4:36PM |
EE.00002: Streamwise vortices in shear flows: Stability of the lower branch states in Couette flow Phil Hall, Spencer Sherwin The relationship between asymptotic descriptions of vortex-wave interactions and more recent work on ``exact coherent structures'' is investigated. We have recently shown that the so-called ``lower branch'' state, which has been identified as playing a crucial role in these self-sustained processes is a finite Reynolds number analogue of a Rayleigh vortex-wave interaction with scales appropriately modified from those for external flows to Couette flow the flow of interest here. Remarkable agreement between the asymptotic theory and numerical solutions of the Navier Stokes equations is found even down to relatively small Reynolds numbers thereby suggesting the possible importance of vortex-wave interaction theory in turbulent shear flows. In this talk we will discuss the stability of the lower branch states for Couette flow where we will show that there is a single unstable mode with growth rate proportional to the Reynolds number raised to the power $-1/2$. The instability is concentrated in a layer which surrounds the critical layer and destroys the wave leaving the roll/streak flow to decay on a $1/R$ timescale. \\[4pt] {\sc Hall, P. \& Sherwin, S.J. } 2010, Streamwise vortices in shear flows: harbingers of transition and the skeleton of coherent structures, {\em J. Fluid Mech.\/} {\bf in press}. [Preview Abstract] |
Sunday, November 21, 2010 4:36PM - 4:49PM |
EE.00003: Streamwise vortices in shear flows: harbingers of transition and the skeleton of coherent structures Spencer Sherwin, Phil Hall The relationship between asymptotic descriptions of vortex-wave interactions and more recent work on ``exact coherent structures'' is investigated. We have recently shown that the so-called ``lower branch'' state, which has been identified as playing a crucial role in these self-sustained processes, is a finite Reynolds number analogue of a Rayleigh {\em vortex-wave interaction} with scales appropriately modified from those for external flows to Couette flow the flow of interest here. Remarkable agreement between the asymptotic theory and numerical solutions of the Navier Stokes equations is found even down to relatively small Reynolds numbers thereby suggesting the possible importance of vortex-wave interaction theory in turbulent shear flows. In this paper we will outline the motivation behind the asymptotic analysis and computational modelling which demonstrate the linkage between wave vortex interaction and self sustaining processes. The minimum drag configuration associated with a fixed spanwise wavenumber is also determined as a function of the downstream wavelength and this points to the crucial importance of long waves evolving on the spatial scale appropriate to the roll/streak flow. \\[4pt] {\sc Hall, P. \& Sherwin, S.J. } 2010, Streamwise vortices in shear flows: harbingers of transition and the skeleton of coherent structures, {\em J. Fluid Mech.\/} {\bf in press}. [Preview Abstract] |
Sunday, November 21, 2010 4:49PM - 5:02PM |
EE.00004: Critical layer structure in transitional Couette flows Hugh Blackburn, Philip Hall, Spencer Sherwin A recent theoretical/numerical investigation (Hall \& Sherwin 2010) demonstrates that vortex-wave interaction in the critical layer of a roll-streak system provides a driving mechanism that will maintain the coupled flow system in near-equilibrium. In addition the predictions made for the variation in the strength of the roll-wave system with Reynolds number asymptotically match those for the lower-branch states observed by Wang et al.\ (2007) in the Couette system. We use DNS of transitional Couette flows to examine two key predictions made by the theory. First, for fixed spanwise periodic wavelength, we examine the maximum streamwise periodic wavelength for which the flow does not relaminarize, since the theory suggests a wavelength below which equilibrium cannot be maintained. Second, we extract Reynolds stresses in the critical layer, and examine their relationship to observed roll structures, since the theory predicts that rolls are maintained by tangential gradients of Reynolds stress within the critical layer. \newline Hall P \& Sherwin SJ (2010), Streamwise vortices in shear flows: harbingers of transition and the skeleton of coherent structures, \textsl{J Fluid Mech}. In press. \newline Wang J, Gibson J \& Waleffe F (2007), Lower branch coheremt states in shear flows: transition and control, \textsl{Phys Rev Let} \textbf{98}, 204501. [Preview Abstract] |
Sunday, November 21, 2010 5:02PM - 5:15PM |
EE.00005: Vorticity Fluctuations in Plane Couette Flow Jose Ortiz De Zarate, Jan V. Sengers In this presentation we evaluate the flow-induced amplification of the thermal noise in plane Couette configuration. The physical origin of the noise is the random nature of molecular collisions, that contribute with a stochastic component to the stress tensor (Landau's fluctuating hydrodynamics). This intrinsic stochastic forcing is then amplified by the mode- coupling mechanisms associated to shear flow. In a linear approximation, noise amplification can be studied by solving stochastic Orr-Sommerfeld and Squire equations. We compare the efficiency of the different mechanisms, being the most important the direct coupling between Squire and Orr-Sommerfed equations. The main effect is to amplify wall-normal vorticity fluctuations with an spanwise modulation at wave number around 1.5, a configuration that resembles the streaks that have been proposed as precursors of the flow instability. [Preview Abstract] |
Sunday, November 21, 2010 5:15PM - 5:28PM |
EE.00006: Nonlinear stability, bifurcation and resonance in granular plane Couette flow Priyanka Shukla, Meheboob Alam A weakly nonlinear stability theory is developed to understand the effect of nonlinearities on various linear instability modes as well as to unveil the underlying bifurcation scenario in a two-dimensional granular plane Couette flow. The relevant order parameter equation, the Landau-Stuart equation, for the most unstable two-dimensional disturbance has been derived using the amplitude expansion method of our previous work on the shear-banding instability.\footnote{Shukla and Alam, {\emph{Phys. Rev. Lett.}} {\bf{103}}, 068001 (2009). Shukla and Alam, {\emph{J. Fluid Mech.}} (2010, accepted).} Two types of bifurcations, Hopf and pitchfork, that result from travelling and stationary linear instabilities, respectively, are analysed using the first Landau coefficient. It is shown that the subcritical instability can appear in the linearly stable regime. The present bifurcation theory shows that the flow is subcritically unstable to disturbances of long wave-lengths ($k_x\sim 0$) in the dilute limit, and both the supercritical and subcritical states are possible at moderate densities for the dominant stationary and traveling instabilities for which $k_x=O(1)$. We show that the granular plane Couette flow is prone to a plethora of resonances.\footnote{Shukla and Alam, {\emph{J. Fluid Mech.}} (submitted, 2010)} [Preview Abstract] |
Sunday, November 21, 2010 5:28PM - 5:41PM |
EE.00007: Chaotic synchronization of the wall turbulence Sedat Tardu Multiscale edge detection wavelet analysis is applied to the streamwise velocity fluctuations in the buffer layer through direct numerical simulations. The wavelet coefficients are rewritten using analytic signal approach to sort out their local amplitudes and wavenumbers. Large zones of approximately constant wavenumbers have been identified at different scales, and a parallelism is constructed between these observations and stochastic synchronization phenomena. The results we analyze strongly suggest that the wall turbulence is chaotically synchronized with the forcing induced by convecting coherent vortices near the wall, thus comforting our earlier results based on experimental velocity and wall shear stress time series (Tardu, Phys. Fluids, 2007). The spatial extend of phase-locked, synchronized zones feature a clear type I intermittency behaviour. The local amplitude intermittency in the synchronized zones is low, and the small-scale amplitude intermittency increases significantly when they are suppressed. The type I intermittency disappears in the viscous and log layers. These results suggest some wall turbulence control strategies that are similar to chaos control methodology (Tardu, Chaos 2010). [Preview Abstract] |
Sunday, November 21, 2010 5:41PM - 5:54PM |
EE.00008: Development of anisotropy in a spanwise rotating channel Sedat Tardu, Julien Baerenzung Development of anisotropy in a spanwise rotating channel is analyzed in time and space through direct numerical simulations. The aim is to understand how the anisotropy sets-up both in time and space in a supercritical flow, the role of rotation being rather generic in this particular context. A perturbation in the form of a quasi-streamwise pair of vortices is followed in time and space Several techniques to quantify anisotropy are used such as the trajectories in time and space of the Lumley invariants, the dissipation tensor invariants and local anisotropy characterization in spectral domain. The analysis of the shear stress and dissipation tensors invariants shows that the local perturbations ``hesitate'' between a 2 component and a rod-like axisymmetric structure near the channel centerline. The return to isotropy in the outer layer takes time with large excursions appearing in the invariants space. There is no such hesitation near the wall$, $and the excursions take place along 2 component to one component axisymmetric line The local anisotropy is further analyzed by computing the invariants of the amplitude of shear stress Fourier transforms. The invariants of the related spectral tensor is highly intermittent and has a granular structure. A model based on a nonlinear (Duffing) oscillator predicts satisfactorily well the temporal development of the invariants in the outer layer. [Preview Abstract] |
Sunday, November 21, 2010 5:54PM - 6:07PM |
EE.00009: ABSTRACT WITHDRAWN |
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