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 A10: Instability: Jets, Wakes and Shear Layers I |
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Chair: Colm-cille Caulfield, BP Institute and DAMTP Cambridge Room: 25C |
Sunday, November 18, 2012 8:00AM - 8:13AM |
A10.00001: Nonlinear destabilization of stably stratified shear flow Nadia Mkhinini, Thomas Dubos, Philippe Drobinski The supercritical or subcritical nature of the bifurcation occurring at a critical bulk Richardson Ric in stratified shear flows is investigated. This investigation is motivated by the recent observation that, in the stratified Ekman boundary layer, both supercritical and subcritical bifurcations occur for low and high values of the Prandtl number Pr, respectively. Linear stability of stratified shear flows is well-described by the Miles-Howard criterion, but the nature of bifurcation is determined by stabilizing or destabilizing nonlinear feedback mechanisms. To identify such mechanisms, an amplitude equation is derived near Ric. The variations of the first Landau coefficient mu as a function of Reynolds number, Prandtl number and wave vector of the shear instability are studied. Pr is the leading factor determining the sign of mu and the nature of bifurcation. The underlying mechanism is that vertical mixing induced by shear instability reduces background gradients of both velocity and buoyancy. The shear-induced feedback is stabilizing while the stratification-induced feedback is destabilizing and stronger when diffusion is low and Pr is high. The weakly nonlinear analysis is repeated on the continuously stratified Kelvin-Helmholtz flow with identical conclusions. [Preview Abstract] |
Sunday, November 18, 2012 8:13AM - 8:26AM |
A10.00002: On the dynamics of shear layers formed on the interface between a porous strip and a clear fluid Panagiotis-Dimitrios Antoniadis, Miltiadis V. Papalexandris In this talk we present results from 2D and 3D simulations of a temporally-evolving shear layer that is developed on the interface between a porous strip of large porosity and a clear fluid. The simulations are based on a single set of governing equations, valid for both inside and outside the porous layer, that does not require additional conditions on the interface. These equations are integrated via a predictor-corrector, projection-based scheme on a collocated grid. According to our study, the evolution of the shear layer can be divided in 4 phases. The first one is characterised by the onset of the Kelvin-Helmholtz instability, whereas in the second, the layer's momentum thickness grows according to the square-root of time law. The third phase is marked by roll-up and formation of vortices that extend to the interior of the porous medium; nonetheless the spatially-averaged velocities remain self-similar. In the fourth phase, the growth rate is much higher and the flow eventually experiences a transition to turbulence. Our talk concludes with results from a parametric study with respect to the porosity of the porous strip. [Preview Abstract] |
Sunday, November 18, 2012 8:26AM - 8:39AM |
A10.00003: Oblique laminar-turbulent interfaces in plane shear flows Yohann Duguet, Philipp Schlatter In many wall-bounded shear flows, turbulence can spread in the presence of finite-amplitude perturbations despite the linear stability of the base flow. The onset of the transitional regime is usually characterised by the formation of large-scale oblique patterns of alternatively laminar and turbulent flow. Yet the mechanism responsible for the observed obliqueness has so far remained mysterious. In this talk we will focus on the formation of such oblique structures in plane Couette flow, using both analytical arguments and intensive direct numerical simulations. We will suggest a robust mechanism for the obliqueness of the incipient turbulent spots derived from mass and momentum budgets in the regions close to the laminar/turbulent interfaces. [Preview Abstract] |
Sunday, November 18, 2012 8:39AM - 8:52AM |
A10.00004: Gravity, surfactants and interfacial instabilities of shear flows David Halpern, Alexander Frenkel, Adam Schweiger We study the linear-stability properties of slow two-fluid plane Couette-type flows in the presence of gravity and surfactants. If gravity is absent, the flow is unstable in certain regions of parameter space due to insoluble surfactants, while in other parametric regions, surfactants are stabilizing; in the absence of surfactants, gravity may lead to the Rayleigh-Taylor instability while it is stabilizing if the lighter liquid is the top layer. Due to the surfactant, there are two active normal modes, and thus two dispersion curves. For small enough Marangoni numbers Ma, the instability, if any, is longwave at its onset (reported earlier). At larger Ma, the instability close to its onset may be ``midwave,'' where the growth rate is positive for a finite interval of nonzero wavenumbers. We present arbitrary-wavenumber results that involve the Bond number, Ma, the velocity-shear, the viscosity ratio and the aspect ratio of the two layers. We also present results for the special limit of infinite aspect ratio. There are dispersion curves with two maxima - a result of the crossing and reconnection of the dispersion curves as Ma or another parameter varies. Also, as Ma increases, for fixed values of the other parameters, the flow instability may switch on and off multiple times. [Preview Abstract] |
Sunday, November 18, 2012 8:52AM - 9:05AM |
A10.00005: Trailing edge effect on fast mixing in forced confined mixing layers Wei Zhao, Guiren Wang It was believed that due to nonlinear effect and saturation, the spreading rate in forced 2D mixing layers can only reach about two times of that in the unforced one. The limited enhancement restricted the related technique in practical application. We found recently that confined mixing layer can overcome the saturation under a specific and narrow frequency band to achieve ultra fast mixing. Here, we report the spanwise vortices are extremely sensitive to the sharpness of the trailing edge. Without trailing edge, there are no spanwise vortices. In a blunt trailing edge, there can be spanwise wortices, but there is no spanwise counter-rotation vortice. With sharp trailing edge, there are large spanwise vortices and at high forcing level counter-rotation vortices, which can cause initially fast mixing. The influence of trailing edge sharpness on this spanwise counter-rotation shredding vortices could be explained by the relation between acoustic particle displacement (APD) and the curvature radius of trailing edge. When the APD becomes larger or equal to the radius of curvature, the acoustically induced shredding vortices emerge due to the friction of wall and nonlinear flow. That could be why sharper trailing edge can induce strong vortices and fast mixing. [Preview Abstract] |
Sunday, November 18, 2012 9:05AM - 9:18AM |
A10.00006: Transient perturbation growth in time-dependent mixing layers C.P. Caulfield, Cristobal Arratia, Jean-Marc Chomaz We investigate numerically the transient linear growth of three-dimensional perturbations in homogeneous time-evolving hyperbolic tangent mixing layers. We identify perturbations, which are optimal in terms of their kinetic energy gain, over a range of finite, predetermined time intervals. We consider a time-dependent two-dimensional base flow associated with the growth and nonlinear saturation of two wavelengths of the classical ``Kelvin-Helmholtz instability'' (KHI), allowing for the eventual merger of two elliptical KHI billows into a larger single elliptical vortex. If the time-evolving flow actually involves substantial evolution of the primary KHI during the optimization time interval, two broad classes of inherently 3D linear optimal perturbations arise, associated at low wavenumbers with the well-known core-centred elliptical translative instability, and at higher wavenumbers with the braid-centred hyperbolic instability. The growth of the elliptical secondary perturbations is strongly suppressed during primary KHI merger, due to the significant disruption of the primary billow cores, while hyperbolic perturbations, localized in the braid region between the two merging KHI billows, can still undergo significant transient energy growth. [Preview Abstract] |
Sunday, November 18, 2012 9:18AM - 9:31AM |
A10.00007: Minimal seeds in mixing layers Samuel Rabin, Colm Caulfield, Richard Kerswell Recent studies on transition have investigated the nonlinear transient growth properties of the Navier-Stokes equations by using variational techniques to optimize perturbation structure in order to reveal the ``minimal seed'' for turbulence (Cherubini et al 2010, Monokrousos et al 2011, Pringle et al 2012). These studies were performed on geometries and Reynolds numbers that were linearly stable, yet experimental results demonstrated could transition to turbulence, such as Plane Couette Flow (PCF). In contrast to PCF, one of the most commonly studied transition mechanisms is the Kelvin-Helmholtz instability (KHI) of inflectional shear layers, which layers can be shown to be unstable to infinitesimal perturbations for quite moderate Reynolds numbers. In this study, we apply the recently developed variational techniques to optimize the kinetic energy over finite time horizons of three-dimensional finite amplitude perturbations for a time-evolving background flow initially described by a hyperbolic tangent function, which flow is subject to KHI. Our objective is to determine what are the minimal energy perturbations which can trigger turbulence in this geometry, and what role is played by KHI in such ``optimized'' transition. This research was supported by EPSRC. [Preview Abstract] |
Sunday, November 18, 2012 9:31AM - 9:44AM |
A10.00008: The mixing layer downstream of a ``$\Lambda$''-notched splitter plate Lutz Taubert, Emile Suehiro, Israel Wygnanski The turbulent mixing layer created downstream of a ``$\Lambda$''-notched splitter plate that was aligned with the free stream and whose trailing edge was inclined at 60$^{\circ}$ to the flow was investigated experimentally at two velocity ratios. It was observed that the rate of spread of this mixing layer relative to its local center was identical to the rate of spread of a two dimensional mixing layer provided all distances were measured from the trailing edge. Harmonic excitation was applied to this base flow by means of flaperons mounted on the trailing edges of the splitter plate. The external excitation enabled the separation of the instability wave fronts originating from the two opposing trailing edges of the ``$\Lambda$''-notch. The effects of excitation frequency, amplitude and phase between the oscillating flaperons on the spreading rate and the orientation and velocity of the large coherent structures in the mixing layer were determined and the variation of the wave front angles was analyzed along their paths. [Preview Abstract] |
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