Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session G16: Flow Instability: General II |
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Chair: Nathaniel Barlow, Rochester Institute of Technology Room: 204 |
Monday, November 23, 2015 8:00AM - 8:13AM |
G16.00001: Algorithm for spatio-temporal analysis of the signaling problem Nathaniel Barlow, Brian Helenbrook, Steven Weinstein The response of convectively unstable flows to a localized oscillatory forcing (i.e. the “signaling problem”) is studied. The full mathematical structure of this class of problems is elucidated by examining partial differential equations of second (the linear Ginzburg-Landau equation) and fourth order in space. The long-time asymptotic behaviors of the Fourier-Laplace integral solutions are obtained via contour integration and the method of steepest descent. In the process, a general algorithm is developed to extract the important physical characteristics of such problems. The algorithm allows one to determine the velocities that bound the transient and spatially growing portions of the response, as well as a closed-form transfer function that relates the oscillatory disturbance amplitude to that of the spatially growing solution. A new velocity is identified that provides the most meaningful demarcation of the two regions. The algorithm also provides a straightforward criterion for identifying “contributing” saddles that determine the long-time asymptotic behavior and “non-contributing” saddles that give errant solutions. Lastly, a discontinuity that arises in the long-time asymptotic solution, identified in prior studies, is resolved. [Preview Abstract] |
Monday, November 23, 2015 8:13AM - 8:26AM |
G16.00002: Perturbation Enstrophy Decay in Poiseuille and Couette Flows according to Synge's Method Loris Domenicale, Federico Fraternale, Gigliola Staffilani, Daniela Tordella In this work we derive the conditions for no enstrophy growth for bidimensional perturbations in the plane Couette and Poiseuille flows. We follow the method of vorticity proposed by Synge in 1938 (see the Semi-Centennial Puplication of the Amer. Math. Soc., equation 12.13, and the more detailed version in the Proc. of the Fifth Inter. Congress of Applied Mechanics, pages 326-332), which is actually based on the analysis of the spatially averaged enstrophy. We find that the limit curve in the perturbation wavenumber-Reynolds number map differs from the limit for no energy growth (see e.g. Reddy 1993). In particular, the absolute stability region for the enstrophy is wider than that of the kinetic energy, and the maximum Reynolds number giving the monotonic enstrophy decay, at all wavenumbers, is 155 and 80 for the Poiseuille and Couette flows, respectively. It should be noted that in past literature the energy-based analysis was preferred to Synge's enstrophy analysis. This, possibly, for two reasons: the low diffusivity of the 1938 Vth ICAM proceedings and the objectively very complicated analytical treatment required. Nevertheless, the potentiality of this method seems high and therefore it is interesting nowadays to exploit it by means of the symbolic calculus. [Preview Abstract] |
Monday, November 23, 2015 8:26AM - 8:39AM |
G16.00003: Instabilities and transient growths of the Taylor-Couette flow in stratified fluids Junho Park, Paul Billant, Jong-Jin Baik The Taylor-Couette flow is centrifugally unstable in inviscid limit if $\mu <\eta^{2}$ where $\mu =\Omega_{o} /\Omega_{i} $ and $\eta =r_{i} /r_{o} $ are the ratios of angular velocity and radius between inner and outer cylinders, respectively. In the presence of stable density stratification in axial direction, there is a new instability called Strato-Rotational Instability (SRI) due to the gravity wave resonance between the two cylinders. The SRI can occur in a wider regime of $\mu $ than the Centrifugal Instability (CI) such that the stratified Taylor-Couette flow is always unstable except for the solid-body rotation. Moreover, in the regime of CI, both instabilities co-exist and dominance of these instability changes depending on the stratification. In this presentation, we will show some parametric study results on how these two instabilities behave. Moreover, it is important to study transient growth since it can be a candidate to explain subcritical transitions to turbulence in the stable regime. We will present how the transient growth behaviors change for the stratified Taylor-Couette flow in terms of effects of the stratification on the transient growth which can be explained by two different mechanisms. [Preview Abstract] |
Monday, November 23, 2015 8:39AM - 8:52AM |
G16.00004: Interfacial instabilities and Kapitsa pendula Madison Krieger Determining the critera for onset and amplitude growth of instabilities is one of the central problems of fluid mechanics. We develop a parallel between the Kapitsa effect, in which a pendulum subject to high-frequency low-amplitude vibrations becomes stable in the inverted position, and interfaces separating fluids of different density. It has long been known that such interfaces can be stabilized by vibrations, even when the denser fluid is on top. We demonstrate that the stability diagram for these fluid interfaces is identical to the stability diagram for an appopriate Kapitsa pendulum. We expand the robust, ``dictionary"-type relationship between Kapitsa pendula and interfacial instabilities by considering the classical Rayleigh-Taylor, Kelvin-Helmholtz and Plateau instabilities, as well as less-canonical examples ranging in scale from the micron to the width of a galaxy. [Preview Abstract] |
Monday, November 23, 2015 8:52AM - 9:05AM |
G16.00005: Variational approach to stability boundary for the Taylor-Goldstein equation Makoto Hirota, Philip J. Morrison Linear stability of inviscid stratified shear flow is studied by developing an efficient method for finding neutral (i.e., marginally stable) solutions of the Taylor-Goldstein equation. The classical Miles-Howard criterion states that stratified shear flow is stable if the local Richardson number $J_R$ is greater than 1/4 everywhere. In this work, the case of $J_R>0$ everywhere is considered by assuming strictly monotonic and smooth profiles of the ambient shear flow and density. It is shown that singular neutral modes that are embedded in the continuous spectrum can be found by solving one-parameter families of self-adjoint eigenvalue problems. The unstable ranges of wavenumber are searched for accurately and efficiently by adopting this method in a numerical algorithm. Because the problems are self-adjoint, the variational method can be applied to ascertain the existence of singular neutral modes. For certain shear flow and density profiles, linear stability can be proven by showing the non-existence of a singular neutral mode. New sufficient conditions, extensions of the Rayleigh-Fjortoft stability criterion for unstratified shear flows, are derived in this manner. [Preview Abstract] |
Monday, November 23, 2015 9:05AM - 9:18AM |
G16.00006: Nonlinear evolution of an isolated disturbance at two-phase flow interface Gennaro Coppola, Francesco Capuano, Luigi de Luca The nonlinear evolution of an isolated, finite-amplitude disturbance at the interface between two immiscible fluids of different density is simulated by means of a discrete vortex method. In contrast to the more standard periodic disturbance, that evolves into the familiar train of Kelvin-Helmholtz (KH) linear waves, the single-wave scenario possess unique features that are not yet well known. The aim of the present contribution is to provide a physical modeling of the nonlinear wave evolution, and to highlight the features that distinguish the nonlinear case from the classical KH model. Numerical simulations are carried out as well. The two-phase interface is represented by a discrete vortex sheet, whose dynamics is simulated by a point vortex method that accounts for density stratification, surface tension and gravity. It is found that the nonlinear wave speed is different from the one predicted by the classical KH theory, as a consequence of the different topology of streamlines. The instability onset threshold, as well as other flowfield properties also change accordingly. [Preview Abstract] |
Monday, November 23, 2015 9:18AM - 9:31AM |
G16.00007: The effect of compressibility on magnetohydrodynamic jets and Kelvin-Helmholtz instability Divya Sri Praturi, Sharath Girimaji We investigate the effect of compressibility and magnetic field on the evolution of planar magnetohydrodynamic (MHD) jets. These jets are susceptible to Kelvin-Helmholtz (KH) instability when subjected to an in-plane transverse velocity perturbation. Various linear stability analyses have shown that compressibility and magnetic field along the jet have a stabilizing influence on the KH instability. We performed three-dimensional numerical simulations using magneto gas kinetic method (MGKM) to study the effect of the Mach number, Alfv\'en Mach number, and the orientation of the magnetic field with respect to the jet velocity direction on the flow-field evolution. In MGKM, the magnetic effects are added as source terms in the hydrodynamic gas kinetic scheme which also take into account the non-ideal MHD terms for finite plasma conductivity and the Hall effects. An in-depth analysis of linear and nonlinear physics is presented. [Preview Abstract] |
Monday, November 23, 2015 9:31AM - 9:44AM |
G16.00008: Kelvin-Helmholtz Instability in Compressible Flows and Mixing Inhibition Mona Karimi, Shararath Girimaji It is well-established that the Kelvin-Helmholtz (KH) instability is central to shear flow mixing. Toward understanding the suppression of turbulent mixing under the influence of compressibility, we first examine the modification to KH instability in a planar mixing layer at high speeds. In this presentation, combining the outcomes of the linear stability analysis with the results of the numerical simulation, we establish that the flow domain can be classified into two main regions: the outer regions on the fast and slow sides and dilatational interface layer (DIL) in the middle. Compressibility engenders the formation of a dilatational or acoustic layer at the high-shear interface between two streams of different speeds. Within the DIL, the velocity perturbations become oscillatory. In the incompressible shear layers, the interface experiences steady vortical motion that entrains fluid from both streams leading to familiar KH behavior. In contrast, in the compressible case, the interface motion is oscillatory inhibiting vortex-merging and roll-up, thereby suppressing entrainment that leads to inhibition of the KH instability. Analysis and illustrations of the constituent mechanisms are presented. [Preview Abstract] |
Monday, November 23, 2015 9:44AM - 9:57AM |
G16.00009: New approach of a traditional analysis for predicting near-exit jet liquid instabilities Guillermo Jaramillo, Steven Collicott Traditional linear instability theory for round liquid jets requires an exit-plane velocity profile be assumed so as to derive the characteristic growth rates and wavelengths of instabilities. This requires solving an eigenvalue problem for the Rayleigh Equation. In this new approach, a hyperbolic tangent velocity profile is assumed at the exit-plane of a round jet and a comparison is made with a hyperbolic secant profile. Temporal and Spatial Stability Analysis (TSA and SSA respectively) are the employed analytical tools to compare results of predicted most-unstable wavelengths from the given analytical velocity profiles and from previous experimental work. The local relevance of the velocity profile in the near-exit region of a liquid jet and the validity of an inviscid formulation through the Rayleigh equation are discussed as well. A comparison of numerical accuracy is made between two different mathematical approaches for the hyperbolic tangent profile with and without the Ricatti transformation. Reynolds number based on the momentum thickness of the boundary layer at the exit plane non-dimensionalizes the problem and, the Re range, based on measurements by Portillo in 2011, is 185 to 600. Wavelength measurements are taken from Portillo's experiment. [Preview Abstract] |
Monday, November 23, 2015 9:57AM - 10:10AM |
G16.00010: Bifurcations in Flow through a Wavy Walled Channel Zachary Mills, Won Sup Song, Alexander Alexeev Using computational modeling, we examine the bifurcations that occur in laminar flow of a Newtonian fluid in a channel with sinusoidal walls, driven by a constant pressure gradient. The lattice Boltzmann method was used as our computational model. Our simulations revealed that for a set of geometric parameters the flow in the channel undergoes multiple bifurcations across the range of flow rates investigated. These bifurcations take the form of an initial Hopf bifurcation where the flow transitions from steady to unsteady. The subsequent bifurcations in the flow take the form of additional Hopf, and period-doubling bifurcations. The type and pressure drop at which these bifurcations occur is highly dependent on the geometry of the channel. By performing simulations to determine the critical pressure drops where bifurcations occur and the type for various geometries we developed a flow regime map. The results are important for designing laminar heat/mass exchangers utilizing unsteady flows for enhancing transport processes. [Preview Abstract] |
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