Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session ET: General Stability I |
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Chair: Giles Brereton, Michigan State University Room: Hilton Chicago Stevens 5 |
Sunday, November 20, 2005 4:10PM - 4:23PM |
ET.00001: Generalized energies for the stability analysis of plane Pouiseuille flow Maria-Vittoria Salvetti, Andrea Nerli, Simone Camarri Classical energetic stability theory fails in the case of plane Pouiseuille flow, leading to a severe underestimation of the critical Reynolds number, since the linearized Navier-Stokes operator is highly non-normal even for moderate Reynolds numbers. Moreover, the non-linear term contribution vanishes, and thus information about the amplitude of critical disturbances is lost. In the present work a procedure is proposed to derive generalized energies to be used in the energetic stability analysis. In particular, it is shown that the classical energy functional can be perturbed, depending on the Reynolds number, in order to bypass the problems related to the non-normality of the operator. When the generalized energies are used instead of the kinetic energy, the non-linear convective term is shown to play a role, and, for each considered Reynolds number, a lower bound for the amplitude of disturbances that may lead to transition is estimated. The proposed generalized energies are described, and results of their application to plane Pouiseuille flow are shown. [Preview Abstract] |
Sunday, November 20, 2005 4:23PM - 4:36PM |
ET.00002: Bifurcation of Longitudinal Vortical Flows in the Plane Poiseuille Flow by the Ghost Effect of Infinitesimal Curvature Toshiyuki Doi, Yoshio Sone Flows of a viscous incompressible fluid between two parallel plates for infinite Reynolds number are studied as the limiting behavior of flows between two coaxial circular cylinders as the radius of the inner cylinder and the Reynolds number tend to infinity simultaneously with the difference of the radii of the two cylinders fixed. When the speed of divergence of the radius is not faster than the order of the Reynolds number squared, the infinitesimal curvature of the plates produces a finite effect on the flow. Owing to this effect, a longitudinal vortical flow is found to bifurcate from the plane Poiseuille flow of a parabolic velocity profile at infinite Reynolds number. The limiting relation between the radius and the Reynolds number that determines the bifurcation point is derived, and the bifurcated flow fields away from the bifurcation point are obtained numerically. [Preview Abstract] |
Sunday, November 20, 2005 4:36PM - 4:49PM |
ET.00003: Secondary optimal growth in channel flows Carlo Cossu, Mattias Chevalier, Dan S. Henningson We compute the linear `secondary' optimal transient energy growth supported by an unsteady optimally growing basic flow in a plane channel. This primary flow is generated by giving as initial condition the Poiseuille solution plus `primary' optimal spanwise periodic vortices of finite amplitude $A_0$ which evolve into transiently growing streaks. For small amplitudes $A_0$ of the primary initial vortices, the secondary optimal perturbations and energy growth are almost identical to the primary ones. For larger amplitudes, however, a distinct strong secondary growth mechanism sets in which is related to the modal secondary instability of the streaks. Therefore, for initial conditions of sufficiently large amplitude, the optimal perturbations leading to maximum transient growth in a plane channel flow do not consist any more in streamwise vortices alone but in more complicated structures. [Preview Abstract] |
Sunday, November 20, 2005 4:49PM - 5:02PM |
ET.00004: Flow structure and stability analysis for back-step flow Adrian Mihaiescu, Horia Hangan, Anthony Straatman, Jose Eduardo Wesfreid The structure and stability of the flow over a backward-facing step are studied using direct numerical simulation. Two-dimensional and three-dimensional simulations are conducted at a Reynolds number between 50 and 600. The reattachment length and velocity profiles are in agreement with the experimental and numerical results reported by J.-F. Beaudoin et al.(2003). The Rayleigh discriminant and the Gortler number are calculated for the stability study. Present results identify the same regions of instability as previously found by the two-dimensional simulations of Beaudoin et al., but the values of both Rayleigh discriminant and Gortler number are significantly different. Two Eckman structures close to the lateral walls, followed inside the flow domain by two Gortler structures, located downstream the step are identified. It is shown that other Gortler structures appear when a spanwise periodic perturbation of the inflow velocity is imposed. However, these longitudinal structures depend on the inflow conditions. [Preview Abstract] |
Sunday, November 20, 2005 5:02PM - 5:15PM |
ET.00005: Observation of near-heteroclinic cycles in the von Karman flow Caroline Nore, Frederic Moisy, Laurent Quartier The bifurcations and the nonlinear dynamics of the von K\'arm\'an swirling flow between exactly counter-rotating disks in a stationary cylinder are experimentally investigated by means of visualizations and particle image velocimetry. A regime diagram of the different flow states is determined as a function of the height-to-radius ratio $\Gamma$ and the Reynolds number $Re$ based on disks rotation speed and cylinder radius. Among the steady and time-dependent states found in the experiment, robust near-heteroclinic cycles, that link two unstable states of azimuthal wavenumber $m=2$, are observed and characterized in detail for $\Gamma = 2$. These are compared with the numerical findings of Nore et al [{\it J. Fluid Mech} {\bf 477}, 51 (2003)], with a particular emphasis on the influence of the imperfection and the noise of the experimental setup. [Preview Abstract] |
Sunday, November 20, 2005 5:15PM - 5:28PM |
ET.00006: Flutter instability of flags for different aspect ratios Christophe Eloy, Claire Souilliez, Lionel Schouveiler We address experimentally and theoretically the flutter instability of a flag in a wind. Clamped-free flags of various surface densities and flexural rigidities have been considered. Although this model problem of fluid-structure interaction has been studied continuously since the pioneering work of Lord Rayleigh in 1879, the existing theoretical models are unable to predict accurately the instability threshold. To take into account the finite aspect ratio of the flags, we have developed a linear model of 2D fluttering coupled to a 3D flow. The aspect ratio is defined as H/L, where H is the flag span and L its length (in the streamwise direction). In the Fourier space, an asymptotic theory is carried out to express the fluid load on the flag as powers of L/H. At first order, we recover the results of existing theories for infinitely extended flags. The second order is found to lower the average pressure on the flag, resulting in a stabilizing effect. The instability threshold is then a decreasing function of H/L in agreement with experimental results. [Preview Abstract] |
Sunday, November 20, 2005 5:28PM - 5:41PM |
ET.00007: Stochastic Thermal Convection Daniele Venturi, Xiaoliang Wan, George Karniadakis Stochastic bifurcations and stability of natural convective flows in 2d and 3d enclosures are investigated by the multi-element generalized polynomial chaos (ME-gPC) method (Xiu and Karniadakis, SISC, vol. 24, 2002). The Boussinesq approximation for the variation of physical properties is assumed. The stability analysis is first carried out in a deterministic sense, to determine steady state solutions and primary and secondary bifurcations. Stochastic simulations are then conducted around discontinuities and transitional regimes. It is found that these highly non-linear phenomena can be efficiently captured by the ME-gPC method. Finally, the main findings of the stochastic analysis and their implications for heat transfer will be discussed. [Preview Abstract] |
Sunday, November 20, 2005 5:41PM - 5:54PM |
ET.00008: Two Types of Linear Theories for Atomizing Liquids S.P. Lin The onset of breakup of liquid jets or sheets is commonly predicted by determining how the infinitesimal disturbance grows with time. This theory is usually called temporal theory. Amore recently developed theory predicts how the disturbance evolves in space and time. The latter theory is termed spatio-temporal theory. This article demonstrates how the temporal theory may mis-predict the nature of the onset of instability. A very important type of instability called absolute instability also instability also escaped totally the prediction of the temporal theory. The mis-prediction and the incompleteness of the temporal theory is demonstrated by use of an example of sheet breakup preceding the atomization. [Preview Abstract] |
Sunday, November 20, 2005 5:54PM - 6:07PM |
ET.00009: Rubber band recoil in fluids Romain Vermorel, Nicolas Vandenberghe, Emmanuel Villermaux The recoil of a stretched rubber band is a familiar phenomenon which does not last for more than a millisecond. When an initially stretched rubber band is released at one end, a front leaving behind it stress-free elastic material propagates towards the clamped end. Its rebound results in a compression front propagating backwards, which triggers an elastic instability referred to as dynamic buckling. High speed movies reveal that the fluid environment affects both the propagation of axial stress waves along the elastic band and the buckling development itself. Our analysis quantifies the impact of a fluid environment on both the rubber motion and on the buckling wavelength selection, in agreement with the experimental findings. [Preview Abstract] |
Sunday, November 20, 2005 6:07PM - 6:20PM |
ET.00010: Impact of noise on the onset of vortex breakdown B.D. Welfert, J.M. Lopez, F. Marques The effects of noise on the onset of vortex breakdown in an enclosed cylinder driven by the rotation of an endwall is investigated using a novel approach in which the stochasticity is introduced physically via the boundary conditions, leading to a system with stochastic parametric forcing. A novel temporal reduction of the stochastic problem to a mean flow problem and a stochastic correction problem involving a random Wiener process whose characteristics explicitly depend on the mean solution and the type of noise, is used in order to make the problem tractable. [Preview Abstract] |
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