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 EL: Instability: General II |
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Chair: John Gibson, Georgia Institute of Technology Room: Salt Palace Convention Center 250 F |
Sunday, November 18, 2007 4:10PM - 4:23PM |
EL.00001: Visualizing the geometry of state space in plane Couette flow John Gibson, Predrag Cvitanovi\'c, Jonathan Halcrow Motivated by recent experimental and numerical studies of recurrent coherent structures in wall-bounded shear flows, we initiate a systematic exploration of the hierarchy of unstable invariant solutions of the Navier-Stokes equations. We construct a dynamical, $10^5$-dimensional state-space representation of plane Couette flow at $Re=400$ in a small, periodic cell and offer a new method of visualizing invariant manifolds embedded in such high dimensions. We compute the leading linearized stability exponents and eigenfunctions of known equilibria at this Reynolds number and cell size. What emerges from global continuations of their unstable manifolds is a surprisingly simple and elegant dynamical-systems visualization of low-Re turbulence. The invariant manifolds tessellate the region of state space explored by transiently turbulent dynamics with a rigid web of heteroclinic connections induced by the continuous and discrete symmetries. [Preview Abstract] |
Sunday, November 18, 2007 4:23PM - 4:36PM |
EL.00002: A multiscale approach to study the stability of long waves in near-parallel flows Stefania Scarsoglio, Daniela Tordella, William Criminale The linear stability of a two-dimensional non-parallel flow is considered as an initial-value problem. A spatio-temporal multiscale approach is assumed. The choice of the polar wavenumber ($k\rightarrow0$) as the small parameter (Blossey, Criminale \& Fisher 2007) leads to a regular perturbation scheme. The introduction, in the perturbation Fourier decomposition, of a complex longitudinal wavenumber (Scarsoglio, Tordella \& Criminale 2007) makes the problem well-posed at any order. By imposing arbitrary three-dimensional disturbances in terms of the vorticity, both the early transient as well as the asymptotic fate can be observed (Criminale \& Drazin 1990). An example concerning the stability of a growing wake is presented (basic flow as $U(x,y), V(x,y)$, Tordella \& Belan 2003). A summary of significant early time transients is shown. In the longitudinal perturbation case, asymptotic temporal results are compared with multiscale normal mode analyses (small parameter $1/R$) for the intermediate and far wake (Tordella, Scarsoglio \& Belan 2006; Belan \& Tordella 2006). [Preview Abstract] |
Sunday, November 18, 2007 4:36PM - 4:49PM |
EL.00003: Long-wave instability of a multicomponent fluid layer with Soret effect Ilya Ryzhkov, Valentina Shevtsova The long-wave instability of a vertical layer filled with a multicomponent fluid is investigated. The basic state is the plane parallel flow, where the linear temperature profile induces linear profiles of composition due to the Soret effect. This effect is characterized by the separation ratios that can be positive or negative depending on the direction of component segregation (to the hot or cold wall). It is shown that the cross-diffusion coefficients can be eliminated by introducing new concentrations and separation ratios. This transformation preserves boundary conditions in a wide class of problems including Rayleigh-Bernard configuration. It allows us to reduce the problem to that without cross-diffusion. The long-wave instability is caused by the interplay between the main flow and the concentration waves, which have a long scale in vertical direction and produce non-uniform density stratification. In the general case of $n$-component mixture, several stable regions in the parameter space are identified. The complete analysis is performed for the ternary fluid case. It is shown that the onset can be monotonic or oscillatory depending on the parameters. The critical Grashof numbers are plotted and their behaviour is discussed. [Preview Abstract] |
Sunday, November 18, 2007 4:49PM - 5:02PM |
EL.00004: Coriolis effects on the elliptical instability in cylindrical and spherical rotating containers Michael Le Bars, St\'ephane Le Diz\`es, Patrice Le Gal The effects of Coriolis force on the elliptical instability are studied experimentally in cylindrical and spherical rotating containers embarked on a table rotating at a fixed rate $\tilde{\Omega}^G$. For a given set-up, changing the ratio $\Omega^G$ of global rotation $\tilde{\Omega}^G$ to flow rotation $\tilde{\Omega}^F$ leads to the selection of various unstable modes due to the presence of resonance bands, in close agreement with the normal mode theory. No instability takes place when $\Omega^G$ ranges between $-3/2$ and $-1/2$ typically. When decreasing $\Omega^G$ toward $-1/2$, resonance bands are first discretized for $\Omega^G>0$ and progressively overlap for $-1/2<\Omega^G<0$. Simultaneously, the growth rates and wavenumbers of the prevalent stationary unstable mode significantly increase, in quantitative agreement with the viscous short--wavelength analysis. New complex resonances have been observed for the first time in the sphere, in addition to the standard spin-over. We argue that these results have significant implications in geo- and astrophysical contexts. [Preview Abstract] |
Sunday, November 18, 2007 5:02PM - 5:15PM |
EL.00005: Linear Stability Analysis Of A Magnetic/Non-Magnetic Fluid Coflow In The Presence Of A Magnetic Field Anindya De, Ishwar Puri Ferrofluids are colloidal suspensions of magnetic nanoparticles in carrier liquids. Being both magnetic and a liquid, they are readily maneuvered from a distance using magnetic fields. When functionalized with different antibodies or medicinal compounds, the ferrofluid can be used for various purposes, e.g., to detect bacteria or for targeted drug delivery. We have considered a coflow where two fluids are separated by a vertical surface parallel to the direction of gravity. For simplicity the flow is assumed to be inviscid and incompressible. We have investigated two configurations depending on the position of the magnet relative to the channel. When the magnet is placed adjacent to the vertical wall along which the magnetic fluid is flowing, the magnetic fluid stays close to the wall unless perturbed by the shear due to a velocity difference. It results in a very stable system. In the second case, the magnet is placed close to the wall along which the non-magnetic fluid flows. The magnetic fluid gets attracted towards the magnet and tries to flow toward it when it gets resisted by the non-magnetic fluid. This configuration is inherently unstable and responds to small perturbations. The surface tension force resists the perturbation of smaller wavelengths. The relative effects of different forces are characterized by magnetic pressure number, Weber number and magnetic Weber number. [Preview Abstract] |
Sunday, November 18, 2007 5:15PM - 5:28PM |
EL.00006: Bulk electroconvective instability at high Peclet numbers Brian Storey, Boris Zaltzman, Isaak Rubinstein Bulk electroconvection pertains to flow induced by the action of a mean electric field upon the residual space charge in the macroscopic regions of a locally quasi-electroneutral strong electrolyte. For a long time, controversy has existed in the literature as to whether quiescent electric conduction from such an electrolyte into a uniform charge selective solid, such as metal electrode or ion exchange membrane is stable with respect to bulk electroconvection. While it was recently claimed that bulk electroconvective instability could not occur, this claim pertained to an aqueous, low molecular weight electrolyte characterized by order unity electroconvection Peclet number. In this work we show that the bulk electroconvection model transforms into the leaky dielectric model in the limit of infinitely large Peclet number. For the leaky dielectric model, conduction of the above mentioned type is unstable, and so it is in the bulk electroconvection model for sufficiently large Peclet numbers. Such instability is sensitive to the ratio of the diffusivity of the cations to the anions. For infinite Peclet number, the case with equal ionic diffusivities is a bifurcation point separating stable and unstable regimes at low current limit. Further, when the Peclet number is finite and the anions are much more diffusive than the cations an unreported bulk electroconvective instability is possible at low current. [Preview Abstract] |
Sunday, November 18, 2007 5:28PM - 5:41PM |
EL.00007: Does thermal explosion really get delayed by natural convection? Mohamed Al-Aseeri, Weidong Guo, Lewis Johns , Ranga Narayanan A thermal explosion is said to occur in a region if heat generated steadily therein cannot be conducted to its boundaries. Our interest is in the effect of natural convection on the conditions for thermal explosion. It is surprising, first, that adding a second mechanism for heat loss lowers the steady rate of heat generation and, second, that natural convection, therefore appears to do little to change the point of explosion. This is due to the fact that the flow, by lowering the heat generation, is self-weakening. [Preview Abstract] |
Sunday, November 18, 2007 5:41PM - 5:54PM |
EL.00008: Formation and Collapse of a depth-limited cavity generated by a supercavitating projectile Derrick Treichler, Ken Kiger, David Han The formation and collapse of the cavity created by the impact of a high-speed projectile entering water is studied experimentally in a 1-meter deep water tank, with a goal of predicting the transient pressure history in the vicinity of the dart impact point. The projectiles were fired vertically using pressurized helium at speeds ranging 200 m/s to 450 m/s. Nose diameters of 6 mm and 12 mm were tested. Projectile motion was captured using a high-speed camera at 5,000 frames per second. Pressure histories were sampled at a rate of 200 kHz at six positions within the tank using piezoelectric transducers. Apparent cavity shapes are digitized from high speed images to produce a time record of cavity radius at each depth in the tank. Results show that the cavity radius scales nominally with the rate of energy loss of the projectile and that the collapse time scales with an adjusted form of Rayleigh's model for the collapse of an infinite cylindrical bubble. [Preview Abstract] |
Sunday, November 18, 2007 5:54PM - 6:07PM |
EL.00009: The Generation of Pressure Waves by the Implosion of Light Bulbs in a High-Pressure Water Environment C. Ikeda, M. Czechanowski, J.H. Duncan The implosion of light bulbs in a high-pressure water environment was studied experimentally in a nearly spherical implosion tank with a nominal internal diameter of 1.77 m. During an experimental run, the light bulb was tethered in the center of the tank which was then filled with water and slowly pressurized by adding nitrogen gas into a small ullage above the water. The gas pressure in the ullage was measured with a slow response transducer and the high-frequency pressure waves in the water were recorded at 14 positions in the tank with underwater blast sensors. The motion of the light bulb was recorded with a high-speed digital movie camera. The implosions occurred at ambient pressures ($P_a$) ranging from 6.1 bar to 11.6 bar. The collapse times of the light bulbs were found to be about 1.3 times the theoretical collapse time of a spherical bubble at the same ambient pressure and with the same radius as the light bulb. The ratio of the peak pressure increase due to the pressure wave at a fixed distance ($r$) from the bubble to the ambient pressure at implosion ($(P(r)-P_a)/P_a$) increased from about 0.5 to 2.7 as the ambient pressure increased over the above-mentioned range. [Preview Abstract] |
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