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 A22: Turbulence Modeling II |
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Chair: Ralph Metcalfe, University of Houston Room: 317 |
Sunday, November 24, 2013 8:00AM - 8:13AM |
A22.00001: By-pass mechanism for transition to turbulence in supercritical pipe flow Ronald J. Adrian, Xiaohua Wu, Parviz Moin, Jon R. Baltzer, Jean-Pierre Hickey Direct numerical simulations of 250R long pipe flows evolving spatially at Reynolds number of 6000 and 8000 show that a thin ring of turbulent fluctuations extracted from a fully turbulent simulation superimposed on the linearly stable parabolic profile is capable of causing transition to the self-sustaining turbulent state. The finite amplitude disturbances from the ring create a roughly annular turbulent wake that grows downstream radially inward and outward. Transition is triggered by vortex filaments drawn from the disturbance region, intensified by stretching, and moving towards the wall. Between 30-40R the filaments induce inward radial flows; in turn, they create lambda or hairpin vortices that rapidly form into hairpin packets. Small-scale activity explodes when the packets create turbulent spots and overcomes larger-scale fluctuations from the initial disturbances as it grows and interacts to fill the pipe with turbulence that approaches the fully developed state by about 75R. Following hairpin formation the process is similar to transition in boundary layers. Unlike boundary layers, there is no stage of linear instability in the pipe, and 2-D and 3-D finite amplitude instabilities near the wall do not appear to play a role. [Preview Abstract] |
Sunday, November 24, 2013 8:13AM - 8:26AM |
A22.00002: Following analytically stages of transition in Couette flow Michael Karp, Jacob Cohen A possible explanation for transition in Couette flow is the mechanism of transient growth (TG). Accordingly, a small disturbance can achieve a significant non-modal TG and trigger nonlinear mechanisms before its eventual decay owing to viscosity. The linear optimal disturbance achieving the maximal growth consists of a pair of streamwise independent counter-rotating vortices (CVPs) which create spanwise-varying streamwise streaks. These may become unstable with respect to infinitesimal disturbances. It is shown that four decaying normal modes, obtained analytically, are sufficient to follow the linear TG mechanism. A secondary linear stability analysis of the modified base-flow (Couette flow with streaks) is conducted using Floquet theory for the spanwise periodic base-flow. The predictions of the stability analysis are compared with direct numerical simulations using the ``Channelflow'' code. It is shown analytically that the inclusion of nonlinear interactions between the base-flow and the CVPs is required in order to predict instability. Furthermore, it is demonstrated that the generation of a `strong' inflectional point is more important than obtaining maximal growth. The minimal number of modes enables us to follow analytically several key stages of the transition process. [Preview Abstract] |
Sunday, November 24, 2013 8:26AM - 8:39AM |
A22.00003: Early stages of transition in viscosity-stratified channel flow Rama Govindarajan, Sharath Jose, Luca Brandt In parallel shear flows, it is well known that transition to turbulence usually occurs through a subcritical process. In this work we consider a flow through a channel across which there is a linear temperature variation. The temperature gradient leads to a viscosity variation across the channel. A large body of work has been done in the linear regime for this problem, and it has been seen that viscosity stratification can lead to considerable changes in stability and transient growth characteristics. Moreover contradictory effects of introducing a non uniform viscosity in the system have been reported. We conduct a linear stability analysis and direct numerical simulations (DNS) for this system. We show that the optimal initial structures in the viscosity-stratified case, unlike in unstratified flow, do not span the width of the channel, but are focussed near one wall. The nonlinear consequences of the localisation of the structures will be discussed. [Preview Abstract] |
Sunday, November 24, 2013 8:39AM - 8:52AM |
A22.00004: Transient growth of disturbances in near-wall region of turbulent channel flow Euiyoung Kim, Haecheon Choi, John Kim The transient growth of optimal disturbances has been suggested as a part of self-sustaining process of turbulent structures. It is generally accepted that the self-sustaining process is independent of the outer part of a boundary layer. In this study, we investigate the relationship between the optimally amplified disturbances in the near-wall region and turbulent structures in turbulent channel flows for $Re_{\tau}=180$ to $10000$. Optimal disturbances in a confined domain ($0 |
Sunday, November 24, 2013 8:52AM - 9:05AM |
A22.00005: Identification of spatially-localized flow structures via sparse proper orthogonal decomposition Neil Dhingra, Mihailo Jovanovic, Peter Schmid Proper Orthogonal Decomposition (POD) has become a standard tool for identification of the most energetic flow structures in fluid flows. It relies on the maximization of a quadratic form subject to a quadratic equality constraint, which can be readily accomplished via a singular value decomposition. For spatially homogeneous (or nearly homogeneous) flows, the resulting flow structures are global (or have large support) in the spatial domain of interest. By augmenting the optimization problem with an additional penalty term that promotes sparsity in the physical space, we are able to obtain energetic flow structures that become increasingly localized as our emphasis on sparsity increases. The resulting optimization problem, formulated in terms of an augmented Lagrangian functional, is solved using the Alternating Direction Method of Multipliers followed by a postprocessing step. The sparse POD algorithm is applied to the linearized Navier-Stokes equations for a plane channel flow, and the emergence of spatially localized structures is observed for increasing penalty terms. This test case and the underlying optimization techniques build the foundation for further studies into the relevance and role of localized perturbations on the overall behavior of general shear flows. [Preview Abstract] |
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