Bulletin of the American Physical Society
2006 APS March Meeting
Monday–Friday, March 13–17, 2006; Baltimore, MD
Session P5: Shedding Light on the Enigma of the Transition to Turbulence in Pipes and other Shear Flows |
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Sponsoring Units: DFD Chair: Tom Mullin, DFD; R.R. Kerswell, Bristol University Room: Baltimore Convention Center 309 |
Wednesday, March 15, 2006 11:15AM - 11:45AM |
P5.00001: The Transition to and from Turbulence in a pipe Invited Speaker: A discussion of experimental investigations of the stability of flow along a pipe will be given. The transition to turbulence is catastrophic when a well--defined amplitude of injected perturbations is exceeded. The stability threshold scales inversely proportional to the Reynolds number, $Re$, with a sharp cut off at low $Re$ values. On the other hand, the decay from the turbulent state exhibits systematic exponential behavior with diverging timescales which are indicative of critical behavior. The long transients contain spatio-temporal coherence which suggest connections with recent theoretical developments. [Preview Abstract] |
Wednesday, March 15, 2006 11:45AM - 12:15PM |
P5.00002: Transient growth and subcritical transition in shear flows Invited Speaker: The possibility for disturbance growth in shear flows which are linearly stable is discussed, and it is shown that a necessary condition is that the underlying linear operator is non-normal, i.e. that it is associated with non-orthogonal eigenfunctions. Since the non-linear terms are conservative it is only by utilizing linear growth mechanisms associated with the non-normal linearized operator that energy growth is possible also for subcritical finite amplitude disturbances. The non-normal effects are manifested in the possibility for large transient growth of the disturbance energy, large response to forcing and large sensitivity of the eigenvalues. The optimal transient growth and response to forcing are calculated as the norm of the matrix exponential and resolvent, respectively. The optimal disturbances are streamwise vortices and the optimal responses are streaks of high and low velocity in the streamwise direction. These flow structures are prevalent in all subcritical transitional shear flows, including pipes and channels. It is shown by direct numerical simulations that transition scenarios initiated by the optimal disturbances have low transition thresholds. The dependence of the thresholds on the Reynolds number is also presented. Finally, extensions of the transient growth concept to more complex flows are discussed and examples of its use given. [Preview Abstract] |
Wednesday, March 15, 2006 12:15PM - 12:45PM |
P5.00003: Self-Sustaining Process and Exact Coherent Structures in Shear Flows Invited Speaker: The Self-Sustaining Process (SSP) is a weakly nonlinear theory of a fundamental three-dimensional nonlinear process in shear flows. It is the basic mechanism that enables enhanced momentum transport and the redistribution of the mean shear energy into smaller scales and, ultimately, turbulent motions. I will briefly review the 40 years of observations of streaks and coherent structures in the near wall region of turbulent shear flows that led to the formulation of the SSP theory. A primary impact of the SSP, besides providing some level of mechanistic understanding, has been to provide a method to calculate unstable traveling wave solutions of the Navier-Stokes equations. This approach has now been successfully carried out in all canonical wall-bounded shear flows with stress as well as velocity boundary conditions. The traveling waves thus obtained show striking similarity with the observed near-wall coherent structures, earning them the name of `exact coherent structures'. Furthermore, those unstable waves have been shown to capture basic statistics of turbulent flows remarkably well, thereby providing hope for a quantitative theory of turbulence over smooth walls. The traveling waves come in many kinds: small scales, large scales and multi-scales. The asymptotics of the large scale traveling waves as the Reynolds number goes to infinity is remarkably simple and confirms the asymptotic validity of the SSP. These large scale coherent states may yield a new promising target for the control of turbulence in shear flows. [Preview Abstract] |
Wednesday, March 15, 2006 12:45PM - 1:15PM |
P5.00004: Travelling waves in pipe flow and their relevance for transition to turbulence Invited Speaker: The problem of understanding the nature of pressure-driven fluid flow through a circular straight pipe remains one of the oldest problems in fluid mechanics. The steady, unidirectional parabolic (laminar) flow solution named after Hagen (1839) and Poiseuille (1840) is linearly stable yet temporally and spatially disordered 3-dimensional (turbulent) solutions can easily be triggered at sufficiently large flow rates (Reynolds 1883). In contrast with Rayleigh-Benard convection where transition to turbulence proceeds along an orderly sequence of bifurcations at well-defined values of the thermal driving, the transition in a pipe is abrupt, dependent on the level of ambient disturbances in the system and, at least close to the threshold flow rate, transient. The recent discovery of travelling wave solutions (which represent saddle points in phase space) in this system has at last provided a theoretical stepping stone towards rationalizing the transition process. We will discuss the structure of these waves as well as evidence of their relevance during the transition process. [Preview Abstract] |
Wednesday, March 15, 2006 1:15PM - 1:45PM |
P5.00005: Two scenarios for dynamics of perturbations in pipe Poiseuille flow Invited Speaker: Two experiments on perturbations in circular pipe flows and their possible theoretical interpretations are discussed to illustrate complexity of the problem. The experimental data by A. Kaskel (1961) are discussed within the framework of spatial transient growth theory, and we argue that the phenomenon of transient growth was observed in the pipe-flow experiments. Another experiment (Eliahou et al, 1998) illustrates how weak streamwise vortices provide instability of the secondary disturbances which, in turn, amplify the steady vertical structures. The latter is consistent with the self-sustaining process scenario. These examples, and more recent DNS and experimental studies represent typical controversies that arise in the study of complex systems. [Preview Abstract] |
Wednesday, March 15, 2006 1:45PM - 2:15PM |
P5.00006: Edge of chaos in the transition to turbulence Invited Speaker: We study the boundary of the laminar region near the onset of turbulence. Approaching the boundary from the laminar side, the lifetime of perturbations increases, diverges when the boundary is reached, and varies chaotically for larger amplitudes. In the chaotic region, lifetimes vary sensitively with amplitude, consistent with the strange saddle picture of the turbulence proposed earlier. The trajectory on the edge between the laminar and chaotic regions is asymptotic to a single well defined state, essentially independent of the type of perturbation. The edge then becomes the stable manifold of this structure. In the case of a model shear flow, the edge states are simple or period doubled or chaotic trajectories. The case of pipe flow shows less variability and the edge state seems to remain close to a state with simple vortical structure. \\ This is joint work with T.M. Schneider (U Marburg), J.D. Skufca (Clarkson U) and J. Yorke (U Maryland). [Preview Abstract] |
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