Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session AI: Instability: Shear Layers I |
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Chair: Francois Blanchette, University of California, Merced Room: Salt Palace Convention Center 250 C |
Sunday, November 18, 2007 8:30AM - 8:43AM |
AI.00001: Stability of a stratified fluid with a vertically moving boundary Francois Blanchette, Tom Peacock, Remi Cousin We present the results of a combined theoretical and experimental study of stratified fluids bounded by a vertically moving side wall. This arrangement is perhaps the simplest in which boundary effects can drive instability and layering in a stratified fluid. It may also be used to investigate the stability of sheared laminar flow augmented of a density gradient. Our investigations reveal that for a given stratification, the side wall boundary-layer flow becomes linearly unstable when the wall velocity exceeds a critical value, which is well below the velocity at which turbulence may be initiated in a uniform fluid. The onset of instability is clearly observed in the experiments, and in many aspects there is quantitative agreement with theoretical predictions. This type of instability is expected to occur frequently in nature owing to the small magnitude of the critical velocity. [Preview Abstract] |
Sunday, November 18, 2007 8:43AM - 8:56AM |
AI.00002: Low-dimensional modeling for both temporally and spatially developing free shear layers Mingjun Wei, Clarence Rowley In this study, both temporally and spatially developing two-dimensional free shear layers are modeled. A modified version of proper orthogonal decomposition/Galerkin projection is used to allow the basis functions to scale along cross-stream direction in time (temporal model) or downstream (spatial model) as the shear layers develop. The solution is scaled at each time (temporal model) or downstream location (spatial model) to match a pre-selected template function. The scaling variable is calculated simultaneously to minimize the difference between the current solution and the template. Projection of incompressible Navier-Stokes equations onto the first two POD modes of the lowest one or two wavenumber/frequency gives a 2-mode or 4-mode temporal/spatial model. It is indicated that at least two POD modes with opposite symmetric behavior are needed to describe the dynamics properly. The incompressibility of each modes is enforced during the scaling, and this turns out to be crucial in successful modeling. [Preview Abstract] |
Sunday, November 18, 2007 8:56AM - 9:09AM |
AI.00003: The two-dimensional mode of the variable-density Kelvin-Helmholtz billow L. Joly, J. Fontane, J.-N. Reinaud We perform a three-dimensional stability analysis of the Kelvin-Helmholtz billow, developing in a shear-layer between two fluids with a density ratio of 3. We begin with 2D-simulations of the temporally evolving mixing-layer yielding the unsteady base flow fields. The Reynolds number is 1500 while the Schmidt and Froude numbers are infinite. Then exponentially unstable modes are extracted from a linear stability analysis. We retain modes growing faster than the primary wave according to a quasi-steady approach. The spectrum is analyzed and shown to exhibit a typical two-dimensional mode, in addition to core-centered and braid-centered ones. This particular mode develops on the baroclinically-enhanced vorticity ridge lying on the light side of the KH-billow. The wavelength of the 2D-instability is ten times shorter than the one of the primary wave. Its amplification rate competes well against the one of the least-stable 3D-modes. The non-linear continuation of this mode is computed from two starting points during the roll-up of the primary wave. We describe secondary roll-ups due to a small-scale Kelvin-Helmholtz mechanism favored by the underlying strain field. This mode is demonstrated consistent with finite Reynolds number mixing-layers. We are also able to discuss its precedence against transverse modes thus contributing to the complex picture of the transition of the variable-density shear-layer. [Preview Abstract] |
Sunday, November 18, 2007 9:09AM - 9:22AM |
AI.00004: Convective instability and transient growth in flow over a backward-facing step Dwight Barkley, Hugh Blackburn, Spencer Sherwin We present transient energy growth of 2D and 3D optimal linear perturbations for flow over a backward-facing step. Reynolds numbers based on the step height and peak inflow speed are considered in the range $0 \leq Re \leq 500$, well below the critical value for the onset of absolute instability. This analysis quantifies for the first time the transient linear response of the flow due to local convective instability downstream of the step edge. The maximum linear transient energy growth is of order $80\times10^3$ at $Re=500$. The critical Reynolds number below which all perturbations decay in energy norm is $Re=57.7$. The centroidal location of the energy distribution for maximum transient growth is typically downstream of all the stagnation/reattachment points of the steady base flow. While their growths are larger, the 3D optimal disturbances are broadly similar in shape to the 2D cases, and the corresponding spanwise wavelengths are of order ten step heights. Nonlinearity is shown to have a stabilizing effect on the instability. [Preview Abstract] |
Sunday, November 18, 2007 9:22AM - 9:35AM |
AI.00005: A Stratified Fluid in the Presence of a Moving Wall: Exact Solutions and their Stability Matthew Moore, Roberto Camassa, Richard McLaughlin, Sorin Mitran, Ashwin Vaidya, Longhua Zhao We present an exact solution for a moving wall in the presence of an unstable density stratification. We discuss the linear stability of the system through the analysis of the associated Orr-Somerfeld type eigenvalue problem. Time permitting, full simulations of the nonlinear system based on pseudospectral projection methods will be presented. [Preview Abstract] |
Sunday, November 18, 2007 9:35AM - 9:48AM |
AI.00006: A numerical study of a two-fluid channel flow instability Siina Haapanen, Brian Cantwell Results from a three-dimensional direct numerical simulation of an initially laminar two-fluid channel flow are presented. The fluids are incompressible and miscible with dissimilar densities and viscosities. They are initially separated by a thin mixed layer, and instability of the flow results in entrainment and mixing of the fluids. In the calculations, perturbations are supplied by linear stability theory, and the temporal evolution of the flow is computed to the non-linear stage. The influence of initial conditions on the subsequent flow evolution is investigated, the effects of fluid density and viscosity ratios and relative depth of the fluid layers are studied, and mixing and entrainment are discussed. [Preview Abstract] |
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