Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session D36: Instability: General I |
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Chair: Cedric Beaume, University of California, Berkeley Room: 407 |
Sunday, November 24, 2013 2:15PM - 2:28PM |
D36.00001: Stability analysis of an impacting T-junction pipe flow Kevin Chen, Clarence Rowley, Howard Stone The flow through a T-shaped pipe bifurcation (with the inlet at the bottom of the ``T'') is a common occurrence in both natural and man-made systems, including blood vessels, industrial pipe networks, and microfluidic channels. Despite the ubiquitous nature of the geometry, many questions about the flow physics remain. We analyze the stability of Navier--Stokes equilibria by executing numerical continuation on the Reynolds number (based on the average inlet velocity), using a combination of linear extrapolation and the Newton--GMRES algorithm. We find that the qualitative nature of the equilibria's local bifurcations is highly sensitive to the grid resolution. On a sufficiently resolved grid, a rapid succession of supercritical Hopf bifurcations begins at $Re \approx 550$. Visualizations of the neutrally stable eigenmodes reveal the physical nature of the instabilities. We also compare equilibria computed with different radii of curvature at the square corners of the ``T.'' Next, a wavemaker analysis reveals the locations in the T-junction where the stability is most sensitive to localized changes in the dynamics, e.g., via a change in geometry. [Preview Abstract] |
Sunday, November 24, 2013 2:28PM - 2:41PM |
D36.00002: Tomographic PIV Observations of the Growth of Localized Perturbations in Transitional Taylor-Couette Flow Daniel Borrero, Michael Schatz The flow between concentric rotating cylinders has been extensively studied over the years. Most studies have focused on the flow patterns that emerge from centrifugal instabilities and at highly turbulent regimes. More recently, however, there has been renewed interest in centrifugally stable Taylor-Couette flows, which bypass linear instability mechanisms and undergo a direct transition to turbulence. This transition shares many features with the direct transition to turbulence in other canonical shear flows that are linearly stable, such as pipe and plane Couette flows, including spatiotemporal intermittency and the coexistence of laminar and turbulent domains. We present tomographic PIV and flow visualization measurements of the growth of finite-size perturbations to the laminar state as they grow into persistent turbulent spots. In particular, we look at how the amplitude and duration of the perturbations affect the transition to turbulence and study the detailed three-dimensional structure of turbulent spots. [Preview Abstract] |
Sunday, November 24, 2013 2:41PM - 2:54PM |
D36.00003: Low-drag exact coherent states in Newtonian channel flow Jae Sung Park, Michael Graham Exact coherent states have been known to nicely capture the main features of turbulent flows such as near-wall coherent structures and streak spacing. In this study, we numerically calculate new classes of exact coherent states, specifically nonlinear traveling wave solutions, for Newtonian channel flow, which display low-drag flow features such as weak streamwise vortices and nearly nonexistent streamwise variations like those observed in polymer solutions and in Newtonian hibernating turbulence. Traveling wave solutions with various symmetries are found. While some of the structures clearly display nonlinear critical layer dynamics, in others this connection is not as clear. Dynamical trajectories are computed and some of the solutions are shown to lie on the basin boundary between laminar and turbulent flows and are thus edge-states of the flow. Lastly, the dependence of Reynolds number for the solutions is investigated. We find one intriguing family whose mean velocity profile appears to approach the so-called maximum drag reduction asymptote found in polymer solutions, despite the fact that fluid studied here is Newtonian. Our results suggest that these traveling wave solutions may play a role as promising targets for turbulence control strategies for drag reduction. [Preview Abstract] |
Sunday, November 24, 2013 2:54PM - 3:07PM |
D36.00004: Exact near-wall traveling waves of plane Poiseuille flow John Gibson, Evan Brand We present several spatially-localized equilibrium and traveling-wave solutions of plane Couette and plane Poiseuille flow. The solutions consist of highly concentrated and spanwise-localized alternating streamwise rolls, centered over low-speed streamwise streaks and flanked on either side by high-speed streaks. For large Reynolds numbers the solutions develop critical layers that are concentrated at isolated points on the critical surface $u=c$. For several traveling-wave solutions of plane Poiseuille flow, the rolls are concentrated near one wall, producing streaks near the wall and larger reduction of the bulk flow in the core. These solutions form particularly isolated and elemental versions of near-wall coherent structures in shear flows and capture, as precise time-independent solutions of Navier-Stokes, the process by which near-wall rolls exchange momentum between the wall and core regions and thereby increase drag. [Preview Abstract] |
Sunday, November 24, 2013 3:07PM - 3:20PM |
D36.00005: A doubly-localized solution of plane Couette flow Evan Brand, John Gibson We present a new equilibrium solution of plane Couette flow localized in two spatially extended directions. The solution is derived from the EQ7/HVS solution of plane Couette flow discovered independently by Itano and Generalis (PRL 2009) and Gibson et al (JFM 2009), of which a spanwise localized version has also recently been produced (Gibson, these proceedings). The doubly localized solution displays relatively long length scales in comparison with the spatially periodic and spanwise localized solutions, suggesting the importance of these scales in capturing the spatial complexity of transitional and low-Reynolds number turbulence. The solution is comparable in size and appearance to the doubly-localized, chaotically evolving edge states previously computed in this flow by Duguet et al (PoF 2009) and Schneider et al (JFM 2010). Additionally, we address the structure of localized solutions in the ``tails,'' i.e. in the region approaching laminar. [Preview Abstract] |
Sunday, November 24, 2013 3:20PM - 3:33PM |
D36.00006: Linear stability analysis of swirling turbulent flows with turbulence models Vikrant Gupta, Matthew Juniper In this paper, we consider the growth of large scale coherent structures in turbulent flows by performing linear stability analysis around a mean flow. Turbulent flows are characterized by fine-scale stochastic perturbations. The momentum transfer caused by these perturbations affects the development of larger structures. Therefore, in a linear stability analysis, it is important to include the perturbations' influence. One way to do this is to include a turbulence model in the stability analysis. This is done in the literature by using eddy viscosity models (EVMs), which are first order turbulence models. We extend this approach by using second order turbulence models, in this case explicit algebraic Reynolds stress models (EARSMs). EARSMs are more versatile than EVMs, in that they can be applied to a wider range of flows, and could also be more accurate. We verify our EARSM-based analysis by applying it to a channel flow and then comparing the results with those from an EVM-based analysis. We then apply the EARSM-based stability analysis to swirling pipe flows and Taylor-Couette flows, which demonstrates the main benefit of EARSM-based analysis. [Preview Abstract] |
Sunday, November 24, 2013 3:33PM - 3:46PM |
D36.00007: Electrokinetic Instability in Plane Poiseuille Flow Lukas Vermach, C.P. Caulfield We consider the linear stability of the flow of an electrically charged liquid driven by a constant pressure gradient through a plane channel with charged walls. The flow is modified by the establishment of electric double layers in the near-wall regions. Chakraborty \& Das (2008 {\it Phys. Rev. E. {\bf 77}} 037303) introduced an extended theoretical model of the associated electroviscous effects, including the streaming field contribution produced as a result of the downstream motion of the charge carriers. We use this model to examine the impact of the streaming field on the background plane Poiseuille flow profile and hence the linear stability of the flow. We find that, under certain realistic circumstances involving sufficiently large surface potential, the streaming field strongly modifies the background flow, inducing inflection points in the velocity profile and near-wall reverse flow. We show that the critical Reynolds numbers for linear instability of such flows are independent of P\'eclet number, and can be substantially suppressed below that of the uncharged classical parabolic flow profile. [Preview Abstract] |
Sunday, November 24, 2013 3:46PM - 3:59PM |
D36.00008: Increasing lifetimes and the growing saddle of shear flow turbulence Tobias M. Schneider, Bruno Eckhardt, Tobias Kreilos In linearly stable shear flows turbulence spontaneously decays on a characteristic transient lifetime. The lifetime sharply increases with Reynolds number so that a possible divergence marking the transition to sustained turbulence at a critical point has been discussed, yet the mechanism underlying the increase has not been understood. We present a mechanism by which the lifetimes increase: a locally attracting orbit forms a ``turbulent bubble'' via a route-to-chaos sequence of bifurcations, followed by a boundary crisis in which the chaotic attractor turns into a chaotic saddle. The complexity of the turbulence supporting saddle hence increases and it becomes more densely filled with unstable periodic orbits, increasing the time it takes for a trajectory to leave the saddle and decay to the laminar state. We demonstrate this phenomenon in the state space of plane Couette flow and show that characteristic lifetimes vary non-smoothly and non-monotonically with Reynolds number. [Preview Abstract] |
Sunday, November 24, 2013 3:59PM - 4:12PM |
D36.00009: Flow Instability and Secondary Vortex Evolution in 90 Degree Bend Lin Niu, Hua-Shu Dou Three-dimensional incompressible Navier-Stokes equations are employed to simulate the laminar flow in a 90 degree bend with square cross-section. Then, the energy gradient theory is used to analyze the stability of the flow. The Reynolds number based on the channel width and the averaged velocity is 158, 394 and 790, respectively. It is found that at Re$=$790, the value of the energy gradient function K increases as the fluid entering the curved section, causing flow instability and forming a pair of secondary vortices; then the secondary vortices gradually stabilizes and the value of K decreases. At the exit of the bend, the total pressure distribution in the cross-section presents serious distortion, which leads to a peak of K. As such, it promotes instability of the flow and causes a transition of two vortices to four vortices. With the flow ahead, the maximum of K in the cross section rises again, resulting in the transition of four vortices to eight vortices. While at low Re (Re $=$ 158 and Re $=$ 394), there is only one pair of vortices in the bend, which are stable, due to low value of K. This study shows that the occurrence of instability is closely related to the evolution of energy gradient function K. [Preview Abstract] |
Sunday, November 24, 2013 4:12PM - 4:25PM |
D36.00010: Kelvin-Helmholtz instabilities and B\'{e}nard Von-Karman Streets under lateral confinement Luc Lebon, Paul Boniface, Mathieu Receveur, Laurent Limat, Fabien Bouillet We have investigated Kelvin-Helmholtz instabilities in a confined geometry. We used a large tank of water with a belt moving at high speed on the central part of its free surface. The water below the belt is dragged by this one, while the excess is recirculating along the lateral walls. Using displaceable walls, belts of different widths, and modifying the water height, it is possible to tune at will the geometry. Depending on the involved ratios, two different behaviors are observed: (1) recirculation by the bottom of the tank, (2) recirculation along the walls with the growth of two coupled Kelvin-Helmholtz instabilities on each side of the belt. At long time scale, and depending again on the involved geometry, the flow evolves to a 3D turbulence or to a well organized B\'{e}nard-Von-Karman street, with a 2D spatial organization of the flow. The wave-length in each vortex row is in agreement with a stability calculations of point vortices developed in the 30's by Rosenhead. [Preview Abstract] |
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