Bulletin of the American Physical Society
61st Annual Meeting of the APS Division of Fluid Dynamics
Volume 53, Number 15
Sunday–Tuesday, November 23–25, 2008; San Antonio, Texas
Session AD: Stability and Transition |
Hide Abstracts |
Chair: Anatoli Tumin, University of Arizona Room: 002B |
Sunday, November 23, 2008 8:00AM - 8:13AM |
AD.00001: Effect of Wall-Temperature Variation in Laminar Boundary Layer Stability Hong Yan, Datta Gaitonde A high-fidelity three-dimensional numerical study is performed to explore the effect of thermal perturbation in a Mach 1.5 flat plate laminar boundary layer. The thermal bump is pulsed at a frequency determined from the linear stability theory. A high-speed and low-speed streaky region is formed downstream in response to the pulsing. The flow stability characteristics are assessed by varying the initial disturbance amplitude, pulsing frequency and the shape of the thermal bump. The rectangular and circular shape are considered. The former one generates two pairs of counter-rotating streamwise vortices at the four edges, while the latter one generates only one pair. The mean flow is greatly distorted, which makes it susceptible to secondary instabilities. The transition mechanism is evaluated using the transient growth and the traditional linear stability theory. [Preview Abstract] |
Sunday, November 23, 2008 8:13AM - 8:26AM |
AD.00002: Experimental investigation of boundary layer transition in the presence of a step Sergiy Gerashchenko, Beverley McKeon, Russell Westphal, Anne Bender, Aaron Drake A fundamental experimental study of the influence of a sharp-edged step on the stability of a laminar boundary layer over a range of step sizes, Reynolds numbers and pressure gradients was performed. The unique test facility, the Towing Wind Tunnel at Tohoku University in Japan, allowed measurements of disturbance growth and transition to be made in a minimal disturbance environment at unit Reynolds numbers of order 10$^{6}$/m. Velocity fluctuations were recorded with an array of hot-wire sensors in the boundary layer downstream of the step, alongside complementary Pitot tube measurements of the mean velocity of the flow. Disturbance spectra, critical transition Reynolds numbers and ``N-factors'' at different flow conditions and step sizes will be discussed. [Preview Abstract] |
Sunday, November 23, 2008 8:26AM - 8:39AM |
AD.00003: Boundary Layer Driven Cavity Flow: Effect of Aspect Ratio Jennifer Wheelus, Pablo Hidalgo, Amy Lang A 2-D, square, transverse cavity model with variable aspect ratio, embedded below a laminar boundary layer, was used to study the formation of Taylor-Gortler like (TGL) vortices through fluorescent dye flow visualization and Digital Particle Image Velocimetry (DPIV). The length to width aspect ratio was varied from 22:1 to 1:1 to evaluate how this affected the formation of secondary TGL vortices within the primary cavity vortex flow field. The results show that for the same freestream velocity, weaker TGL vortices were observed for the lower aspect ratios. In the 1:1 aspect ratio case, no TGL vortices were observed even at the highest freestream velocity. Using the aspect ratio of 22:1, dye visualization was used to study the flow within several adjacent cavities. TGL vortices were not evident in the first two cavities while the third cavity showed definite signs of the beginning stages of TGL vortex formation. Further downstream boundary layer transition was observed, which induced larger velocities inside the cavities and stronger TGL vortices. [Preview Abstract] |
Sunday, November 23, 2008 8:39AM - 8:52AM |
AD.00004: Amplitude Equation for Instabilities Driven at Deformable Surfaces - Rosensweig Instability Harald Pleiner, Stefan Bohlius, Helmut R. Brand The derivation of amplitude equations from basic hydro-, magneto-, or electrodynamic equations requires the knowledge of the set of adjoint linear eigenvectors. This poses a particular problem for the case of a free and deformable surface, where the adjoint boundary conditions are generally non-trivial. In addition, when the driving force acts on the system via the deformable surface, not only Fredholm's alternative in the bulk, but also the proper boundary conditions are required to get amplitude equations. This is explained and demonstrated for the normal field (or Rosensweig) instability in ferrofluids as well as in ferrogels. An important aspect of the problem is its intrinsic dynamic nature, although at the end the instability is stationary. The resulting amplitude equation contains cubic and quadratic nonlinearities as well as first and (in the gel case) second order time derivatives. Spatial variations of the amplitudes cannot be obtained by using simply Newell's method in the bulk. [Preview Abstract] |
Sunday, November 23, 2008 8:52AM - 9:05AM |
AD.00005: Effect of parameter modulation on the dynamo effect in a rapidly rotating spherical shell Vincent Morin The dynamo effect is the process by which the magnetic field of the Earth is generated. In the presence of a small initial magnetic field, convective motions in the fluid outer core produce currents and thus a magnetic field which can reinforce the initial field and sustain it against ohmic diffusion. There is also a feedback of the magnetic field on the flow which limits its growth. Our direct numerical approach consists in solving the equations for the velocity field, the magnetic field and the temperature in a rapidly rotating spherical shell. Convective motions in our system originate from a thermal forcing. The effect on the flow of this forcing can be modulated in time through a modulation of the control parameter. We first focus our study on the impact of this modulation on convection without magnetic field. Depending on parameters and characteristics of the modulation, many interesting features such as shifts of the convective threshold and resonances are found. The magnetohydrodynamic case is then considered. The impact of the parameter modulation on the dynamic of the magnetic field and on the dynamic of reversals of its polarity is studied. [Preview Abstract] |
Sunday, November 23, 2008 9:05AM - 9:18AM |
AD.00006: The Bullard Von K\'arm\'an experiment Gautier Verhille, Mickael Bourgoin, Nicolas Plihon, Jean-Fran\c{c}ois Pinton Since Larmor at the beginning of the XX$^{\circ}$ century, the magnetic field of the earth is thought to be produced from motions of the liquid iron core. Part of the kinetic energy of the flow is converted into magnetic energy. A generic model of the dynamo instability is based on two induction processes, namely $\alpha$ and $\omega$. The $\alpha$- effect is the production of a current density $\vec{j}$ parallel to the initial magnetic field $\vec{b}$, and the $\omega$-effect is linked to the velocity $\vec{v}$ gradients via the term $\vec{b}\cdot\vec\nabla\vec{v}$ in the induction equation. We developed an experimental semi homogeneous $\alpha-\omega$ dynamo (a model commonly used in astrophysics) in a Von K\'arm\'an flow : motion is imparted to liquid Gallium by the counter-rotation of two coaxial impellers with blades. The $\omega$ effect is due to the shear in the mid plane of a Von K\'arm\'an flow and fully includes turbulence. The $\alpha$- effect is simulated by current flow in two coils. Complex dynamics of the dynamo (On-Off intermittency, chaotic reversals, excursions) are observed to be linked with the statistics of the turbulent $\omega$ induction process. [Preview Abstract] |
Sunday, November 23, 2008 9:18AM - 9:31AM |
AD.00007: Stability characteristics of a rotating Poiseuille flow about the streamwise axis Jean-Pierre Hickey, George Khujadze, Martin Oberlack A more complete understanding of transition to turbulence in a Poiseuille flow rotating about the streamwise axis is sought by studying the stability of the flow. Using the classical theory of modal analysis, the stability characteristics of this flow setup are investigated. We find that the addition of the Coriolis force significantly increases the growth rates achieved compared to the non-rotating channel flow until a certain point, after which the high Rossby numbers stabilize the flow. Given the non-normality of the equations governing the flow, we investigate the transient energy growth. We show that the energetic growth can be, as in the non-rotating case, of the order of $O\left(10^3\right)$ and that the maximal growth is caused by disturbances nearly perpendicular to the main flow. The maximal growth is achieved by crosswise perturbations until the point of alpha transition, after which the maximal growth is created by an oblique disturbance. The induced crosswise double-S velocity profile found in previous investigations is explained by the optimal initial disturbances leading to this maximal growth. [Preview Abstract] |
Sunday, November 23, 2008 9:31AM - 9:44AM |
AD.00008: A scenario for transition to turbulence in a rotating boundary layer Bertrand Viaud, Eric Serre, Jean-Marc Chomaz The transition process in a rotating boundary layer is numerically investigated through spectral DNS. The configuration consists of an annular cavity made of two parallel co-rotating disks of finite radial extent, with a forced inflow at the hub and free outflow at the rim. Impulsively disturbed the flow supports a self-sustained saturated wave, matching the description of a nonlinear global `elephant' mode as described by Pier [J.FLUID MECH. 435 135 2001]. This saturated wave is shown to be itself absolutely unstable with respect to secondary perturbations of zero Floquet number, giving birth to a very unorganized state, which can be labeled as turbulent. This scenario relies on a sufficiently strong impulsive perturbation as the first global bifurcation is known to be subcritical (see Viaud, Serre {\&} Chomaz [J.FLUID MECH. 598 451 2008]). On the other hand, strong convective instabilities, in the form of traveling wave packets coming from upstream, are shown to be able to inhibit the formation of the primary front, thus impairing this scenario. [Preview Abstract] |
Sunday, November 23, 2008 9:44AM - 9:57AM |
AD.00009: Stability of the flow past a magnetic obstacle Sergio Cuevas, Alberto Beltran, Eduardo Ramos, Sergey Smolentsev The concept of a magnetic obstacle in an electrically conducting fluid flow refers to the opposing Lorentz force induced by a localized magnetic field that is in relative motion with the surrounding fluid. The name stems from some similarities that occur between the flow past a rigid obstacle and that generated by a localized magnetic field. In this work, the stability of a flow past a magnetic obstacle is described in terms of the Hartmann and Reynolds numbers of the imposed flow (the Hartmann number squared estimates the ratio of magnetic to viscous forces). We find that for a given Hartmann number the flow is steady for small Reynolds numbers and becomes time-dependent, shedding vortices periodically as the Reynolds number grows. But in sharp contrast to the case of a rigid obstacle, for even larger Reynolds numbers, the flow may become steady again. The dependence of the Strouhal number on the governing parameters is also explored. [Preview Abstract] |
Sunday, November 23, 2008 9:57AM - 10:10AM |
AD.00010: Sensitivity Analysis for the Stability and Control of Spiral Vortex Breakdown Elena Vyazmina, Joseph Nichols, Jean-Marc Chomaz, Peter Schmid The physical origin of spiral vortex breakdown is investigated using the direct and adjoint Navier-Stokes equations linearized around axisymmetric vortex breakdown. The axisymmetric solution is computed using a Newton solver for the steady nonlinear Navier-Stokes equations. As a result of the so-called convective non-normality the direct and adjoint global modes for helical perturbations are located downstream and upstream, respectively. In particular, the adjoint mode is dominant in the recirculation bubble where the flow is thus most sensitive to periodic forcing. The wave modes region, defined as the overlap region between the adjoint and direct global modes, allows us to determine whether the wake of the recirculation region or the recirculation region itself causes the spiral vortex breakdown. [Preview Abstract] |
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