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 M6: Nonlinear Dynamics: Transition and Turbulence 
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Chair: Sebastian Altmeyer, Institute of Science and Technology Room: 105 
Tuesday, November 24, 2015 8:00AM  8:13AM 
M6.00001: Invariant solutions organizing turbulence in pipe flow experiments Sebastian Altmeyer, Jakob Kühnen, Markus Schaner, Björn Hof A large number of unstable invariant solutions, e.g. traveling waves (TWs) or (relative) periodic orbits, has been discovered and numerically studied in recent years for pipe flow. The proposed role of such states as building blocks of turbulence is however less clear and so far only limited experimental evidence has been provided. In experiments we used a modulated pipe segment to impose a certain symmetry on the experimental velocity field and in the nonmodulated downstream pipe traveling waves could be observed persisting for many wavelengths. Measured velocity fields (PIV) were used as initial conditions for a numerical Newton search and converged to the exact invariant traveling wave solutions. All the experimentally observed TW's correspond to lower branch states that are close to the laminar turbulent boundary (edge). Correspondingly in the experiments as the waves proceeded downstream flows would typically relaminarize but occasionally the TW's would grow to turbulence. The latter observation confirms the relevance of these invariant states for the transition process. [Preview Abstract] 
Tuesday, November 24, 2015 8:13AM  8:26AM 
M6.00002: Experimental observations of direct laminarturbulent transition in counterrotating TaylorCouette flow Christopher Crowley, Michael Krygier, Daniel BorreroEcheverry, Roman Grigoriev, Michael Schatz The transition to turbulence in counterrotating TaylorCouette flow typically occurs through a sequence of supercritical bifurcations of stable flow states (e.g. spiral vortices, interpenetrating spirals (IPS), and wavy interpenetrating spirals). Coughlin and Marcus have proposed a mechanism by which these laminar spiral flows undergo a secondary instability that leads to turbulence. We report the discovery of a counterrotating regime ($Re_{\textrm{out}} = 1000$, $Re_{\textrm{in}} \approx 640$) of small aspect ratio/large radius ratio TaylorCouette flow ($\Gamma = 5.26$ / $\eta = 0.91$), where the system bypasses the primary instability to stable laminar spirals and instead undergoes a direct transition to turbulence as the inner cylinder rotation rate is slowly increased. This transition is mediated by an unstable IPS state. We study the transition experimentally using flow visualization and tomographic PIV, and show that it is both highly repeatable and that it shows hysteresis as the inner cylinder rotation rate is decreased. As $Re_{\textrm{in}}$ is decreased, the turbulent flow relaminarizes into an intermediate, stable IPS state. Decreasing $Re_{\textrm{in}}$ further returns the system back to circular Couette flow. [Preview Abstract] 
Tuesday, November 24, 2015 8:26AM  8:39AM 
M6.00003: Numerical investigation of direct laminarturbulent transition in counterrotating TaylorCouette flow Michael Krygier, Roman Grigoriev A direct transition from laminar to turbulent flow has recently been discovered experimentally in the smallgap TaylorCouette flow with counterrotating cylinders. The subcritical nature of this transition is a result of relatively small aspect ratio, $\Gamma = 5.26$; for large $\Gamma$ the transition is supercritical and involves an intermediate stable state (Coughlin \& Marcus, 1996)  interpenetrating spirals (IPS). We investigate this transition numerically to probe the dynamics in regimes inaccessible to experiments for a fixed $Re_o=1000$ by varying $Re_i$. The numerics reproduce all the experimentally observed features and confirm the hysteretic nature of the transition. As $Re_i$ is increased, the laminar flow transitions to turbulence, with an unstable IPS state mediating the transition, similar to the TollmienSchlichting waves in plane Poiseuille flow. As $Re_i$ is decreased, turbulent flow transitions to a stable, temporally chaotic IPS state. This IPS state further transitions to either laminar or turbulent flow as $Re_i$ is decreased or increased. The stable IPS state is reminiscent of the preturbulent chaotic states found numerically in plane Poiseuille flow (Zammert \& Eckhardt, 2015), but previously never observed experimentally. [Preview Abstract] 
Tuesday, November 24, 2015 8:39AM  8:52AM 
M6.00004: Rare event statistics and characteristic lifetimes in transient turbulence Tobias Kreilos, Laureline Hentgen, Bruno Eckhardt, Tobias Schneider We numerically study transitional turbulence in plane Couette flow at Reynolds numbers where turbulence is transient. Monitoring the distance to the edge of chaos for a large number of turbulent trajectories, we compute the return period for reaching the vicinity of the edge. The measured return period of the turbulent state is linearly correlated with the characteristic lifetime of the decay. This suggests a way of predicting characteristic lifetime of transient shear turbulence. [Preview Abstract] 

M6.00005: ABSTRACT WITHDRAWN 
Tuesday, November 24, 2015 9:05AM  9:18AM 
M6.00006: System Size Dependence of FiniteAmplitude Thresholds for Transition to Turbulence in TaylorCouette Flow Daniel BorreroEcheverrry, Benjamin Morrison, Evan Peairs Despite centuries of study, fluid dynamicists are still unable to explain why a large class of flows, including pipe flow and plane Couette flow, become turbulent. Hydrodynamic stability theory predicts these flows should be stable to infinitesimal perturbations, which means finiteamplitude perturbations need to be applied to destabilize them. We present the results of a series of experiments studying such subcritical transitions to turbulence in linearlystable configurations of TaylorCouette flow. In particular, we discuss how the stability of these flows depends on the size and duration of the applied perturbation as the aspect ratio of the experimental apparatus is varied. We show that for experimental configurations where the end caps rotate with the outer cylinder, the stability of the flow is enhanced at small aspect ratios. We find that at sufficiently high Reynolds numbers, perturbations must exceed a critical amplitude before the transition to turbulence can be triggered. The scaling of this threshold with Re appears to be different than that which has been reported for other linearlystable shear flows. [Preview Abstract] 
Tuesday, November 24, 2015 9:18AM  9:31AM 
M6.00007: Sudden relaminarisation and lifetimes in forced isotropic turbulence Moritz Linkmann, Alexander Morozov We demonstrate an unexpected connection between isotropic turbulence and wallbounded shear flows. We perform direct numerical simulations of isotropic turbulence forced at large scales at moderate Reynolds numbers and observe sudden transitions from chaotic dynamics to a spatially simple flow, analogous to the laminar state in wall bounded shear flows. We find that the survival probabilities of turbulence are exponential and the typical lifetimes increase superexponentially with the Reynolds number, similar to results on relaminarisation of localised turbulence in pipe and plane Couette flow. Results from simulations subjecting the observed largescale flow to random perturbations of variable amplitude demonstrate that it is a linearly stable simple exact solution that can be destabilised by a finiteamplitude perturbation, like the HagenPoiseuille profile in pipe flow. Our results suggest that both isotropic turbulence and wallbounded shear flows qualitatively share the same phasespace dynamics. [Preview Abstract] 
Tuesday, November 24, 2015 9:31AM  9:44AM 
M6.00008: Disruption of the vortexwave interaction selfsustaining process in stratified plane Couette flow T. S. Eaves, C. P. Caulfield Minimal seeds for turbulence, initial conditions of smallest possible energy density $E_0=E_c$ that eventually transition to turbulence, closely follow the edge manifold in state space before leaving the edge manifold for the turbulent attractor. The trajectories visit a number of coherent states, exact solutions to the NavierStokes equations, that are embedded within the edge manifold. In unstratified plane Couette flow these `edge states' are manifestations of the `selfsustaining process' (SSP) of Waleffe (1997) or the `vortexwave interaction' (VWI) of Hall and Smith (1991). We show that in density stratified plane Couette flow where both a constant, statically stable density difference $2\Delta\rho$ and a constant velocity difference $2\Delta U$ is maintained across a channel of depth $2h$, these states differ from the unstratified states at very small bulk Richardson numbers $Ri_B=g\Delta\rho h/\rho_0\Delta U^2$ (where $g$ is the gravitational acceleration and $\rho_0\gg\Delta\rho$ is a reference density) and that the new states are not of SSP/VWI type. We present a scaling argument to show this is to be expected for $Ri_B\geq O(1/Re)$, where $Re=\Delta Uh/\nu$ and $\nu$ is the kinematic viscosity, and investigate the mechanisms through which the SSP/VWI states breakdown. [Preview Abstract] 
Tuesday, November 24, 2015 9:44AM  9:57AM 
M6.00009: Connecting exact coherent states to turbulent dynamics in channel flow Jae Sung Park, Michael D. Graham The discovery of nonlinear traveling wave solutions to the NavierStokes equations or exact coherent states has greatly advanced the understanding of the nature of turbulent shear flows. These solutions are unstable saddle points in state space, while the time evolution of a turbulent flow is a dynamical trajectory wandering around them. In this regard, it is of interest to investigate how closely the turbulent trajectories approach these invariant states. Here, we present connections between turbulent trajectories and one intriguing solution family in channel flow. A state space visualization of turbulent trajectories is presented in a threedimensional space. The lifetime of the trajectories is well represented by closeness to two distinct solutions resembling in many ways the active and hibernating phases of minimal channel turbulence (Xi \& Graham PRL 2010). The connections are then examined by comparing mean profiles and flow structures. More importantly, the connections are confirmed by calculating the L$_2$ distance between the trajectories and the traveling waves. Lastly, paths of an intermittent bursting phenomenon are identified in state space and the relationship between bursting paths and the traveling waves or hibernating turbulence is further discussed. [Preview Abstract] 
Tuesday, November 24, 2015 9:57AM  10:10AM 
M6.00010: Temporal and spatial intermittencies within Newtonian turbulence Anubhav Kushwaha, Michael Graham Direct numerical simulations of a pressure driven turbulent flow are performed in a large rectangular channel. Intermittent high and lowdrag regimes within turbulence that have earlier been found to exist temporally in minimal channels have been observed both spatially and temporally in fullsize turbulent flows. These intermittent regimes, namely, "active" and "hibernating" turbulence, display very different structural and statistical features. We adopt a very simple sampling technique to identify these intermittent intervals, both temporally and spatially, and present differences between them in terms of simple quantities like meanvelocity, wallshear stress and flow structures. By conditionally sampling of the low wallshear stress events in particular, we show that the Maximum Drag Reduction (MDR) velocity profile, that occurs in viscoelastic flows, can also be approached in a Newtonianfluid flow in the absence of any additives. This suggests that the properties of polymer drag reduction are inherent to all flows and their occurrence is just enhanced by the addition of polymers. We also show how the intermittencies within turbulence vary with Reynolds number. [Preview Abstract] 
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