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14:00   Instability, Transition and Control of Turbulent Flows 2 14:00 15 mins #568 Bursting and amplitude explosions at the onset of turbulent stripes in channel flow Bjorn Hof, Chaitanya Paranjape, Vasudevan Mukund, Nazmi Budanur, Baofang Song, Yohann Duguet Abstract: In channel and Couette flow turbulence first appears in the form of oblique stripes that are surrounded by laminar flow. Stripes are internally chaotic and they spatially arrange in complicated spatio-temporally intermittent patterns. In laboratory experiments stripes display multiple orientations with respect to the mean flow direction and at the lowest Reynolds numbers where stripes are observed the preferred orientation is close to 45 degrees. We next perform direct numerical simulations of turbulent stripes for plane Poiseuille flow in a rectangular domain tilted by 45 degrees with respect to the mean flow direction, and we then reduce the Reynolds number adiabatically. Once Re is reduced below 450 the stripe dynamics begin to considerably simplify, until eventually flows cease to be turbulent and a new exact coherent (laminar) solution of the Navier-Stokes equations is found. Here the flow consists of streaks and vortices arranged in the form of a 45 degree stripe. Dynamically this invariant stripe solution corresponds to a relative periodic orbit. This periodic orbit can be considered as the origin of stripe turbulence for channel flow. With increasing Re it undergoes a secondary Hopf bifurcation to a torus, followed by the appearence of a bursting mode. At this point the fluctuation amplitude suddenly increases by an order of magnitude and the correlation dimension of the resulting chaotic attractor increases rapidly with increasing Re. Eventually the attractor gives way to a chaotic saddle at a boundary crisis. For the selected flow domain we can hence observe the full bifurcation sequence giving rise to turbulent stripes and connect stripe turbulence to the invariant solutions that it originates from. 14:15 15 mins #440 Unsteady localized wave packets in laminar shock-wave/boundary-layer interactions Sébastien Niessen, Koen J. Groot, Stefan Hickel, Vincent E. Terrapon Abstract: The dynamics of the interaction between a developing laminar boundary layer at Mach = 1.7 and an impinging oblique shock-wave with an incident angle of 37.93° is investigated through BiGlobal stability analysis. This approach is motivated by the two-dimensionality of the shock-induced recirculation region. Past stability analyses conducted on the laminar shock-wave/boundary-layer have highlighted the presence of a stationary mode and, more recently, the existence of a convective instability has been demonstrated. However, the latter stability analysis results in eigenmodes that are non-localized in the sense that their support spans the entire domain, from the inlet to the outlet. Therefore, the modes themselves depend noticeably on the artificial truncation boundary conditions. In the present work, we show how the superposition of many non-localized modes can yield a localized wave packet. We specifically investigate how the localized nature of the wave packets impacts the dependency of the results on the truncation boundary conditions. In addition, the results are compared to those obtained with other (non-)local stability analysis methods such as the Parabolized Stability Equations (PSE) and the Wentzel–Kramers-Brillouin-Jeffreys (WKBJ) method. Finally, the proposed approach allows for a boundary-condition-independent characterisation of the stability properties of the shock-wave/boundary-layer interaction. 14:30 15 mins #393 EXPERIMENTS ON LARGE-SCALE FLOWS AROUND TURBULENT SPOTS José Eduardo WESFREID, Lukasz Klotz, Tao Liu, Alexandr Pavlenko, Benoit Semin Abstract: We study localized turbulent spots, surrounded by laminar flow, in the subcritical transition to turbulence in the plane Couette-Poiseuille flow, i.e. of two parallel walls, one moving and the other fixed [1, 2]. The turbulent spots move in confined shear flow with a velocity close to the mean velocity in the gap. This velocity vanishes in this setup, so that we can measure the velocity field in the spot during hundreds of advection times, using time-resolved PIV. We report our experimentally study of the transitional range of Reynolds numbers in plane Couette-Poiseuille flow, focusing our attention on the spots or localized turbulent structures triggered by a normal jet as an impulsive perturbation. We investigate in detail the large-scale flow (LSF) around these localized turbulent structures and the dependence of its amplitude on Reynolds number and the intensity of the perturbation. We consider a large range of the jet amplitudes and in addition we present the characterization of the jet perturbation at Re = 0. We note that in general such experimental measurements are very demanding, which is caused by the weak amplitude of the LSF. As in our case, the advection speed of the flow is greatly reduced, which permits to precisely measure both the spatial and temporal evolution of LSF, which is obtained filtering small and large scales of the measured flow field. In addition, we characterize the dynamics of the turbulent spot by presenting the advection speed and its correlation with the intensity of the LSF. We study the deceleration rate of the localized spot, as well as the estimation of the friction factor corresponding to the force, with which the surrounding laminar flow acts against the turbulent spot. Finally, we also extend our analysis to higher Reynolds numbers when a doubly-localized turbulent spot becomes self-sustained and, for high enough Reynolds number, eventually may turn into a single oblique turbulent band. References [1] L. Klotz, G. Lemoult, I. Frontczak, L.S. Tuckerman, and J. E. Wesfreid. New experiment in Couette-Poiseuille flow with zero mean advection velocity: subcritical transition to Turbulence. Phys. Rev. Fluids, 2: 043904, 2017. [2] L. Klotz and J. E. Wesfreid. Experiments on transient growth of turbulent spots. Journal of Fluid Mechanics, 829, R4, 2017. 14:45 15 mins #460 There and back again, Build up and collapse of transitional plane Couette flow captured by rare events approaches joran rolland Abstract: The scenario of transition to turbulence in wall flows of practical interest (aerodynamic and stably stratified atmospheric boundary layers, flows in the major arteries etc.) are contained in simple academic wall flows such as plane Couette flow. Plane Couette flow is the flow between two planes separated by a distance 2h moving at velocities ±U. The transition in all these flows is controlled by the Reynolds number hU/ with  the kinematic viscosity. Laminar plane Couette flow is linearly stable for all Reynolds numbers, while turbulence can coexist with laminar flow in a quasisteady manner if R > 325 ± 10 and invade the whole flow if R > 400 ± 10. This indicates a situation of bistability between laminar and turbulent flow, with a saddle lying inbetween them, form one point of view or another [4]. Indeed, turbulence can develop if the laminar flow is forced or if an ample enough initial condition is given, while turbulence can collapse under the effect of its own fluctuations to laminar flow if the domain size is finite. In this communication, I will present a numerical study of this bistable situation from the point of view of rare events. This is entirely relevant, since the collapse of turbulence becomes very rare if the Reynolds number and the domain size is increased, and the build up of turbulence from laminar flow becomes very improbable if the variance of the forcing is decreased. I will follow the plan of a previous study [3] and present the computation the rare build up and collapse trajectories, along with their transition rates. For this purpose I used a rare event algorithm termed adaptive multilevel splitting [1] for numerical computations and I used the Freidlin–Wentzell principle of large deviations to discuss the results [5]. In the case of build up of turbulence, I will show the trajectories going from laminar flow to turbulent flow under a wide range of forcing type. I will show that they have instantons properties in the limit of noise variance going to zero. They consist in a fluctuation trajectory under noise toward a saddle point (which has edge stage properties [4]) and then a nearly deterministic relaxation toward turbulence (Fig. 1 (a)). I will show that the chosen saddles and the relaxation paths properties are independent of the noise spectrum : they only depend on the energy injection rate. The entry points toward turbulence are chosen by the dynamics and not the forcing: this is a fully non linear response problem. In the case of collapse of turbulence under its own fluctuations, I will show how one can compute rare event trajectories in the absence of stochastic forcing, using approaches tested in the study of extremes of drag exerted on a blunt body [2]. While trajectories concentrate around specific paths (Fig. 1 (b)), the instanton phenomenology is more complex here: the saddle structure, the “noise” felt by the dynamics all result from turbulence. The numerical approach can nevertheless be used to compute turbulence lifetime as a function of Reynolds number and domain size. 15:00 15 mins #462 Turbulence threshold for plane Poiseuille flow Laurette Tuckerman, Sebastien Gomé, Akshunna Dogra Abstract: The threshold for transition to turbulence in pipe flow has been defined and determined by Avila et al (2011) as the intersection point between two statistically determined timescales, that for decay and that for splitting. A similar calculation has been performed by Shi et al (2013) for plane Couette flow. We investigate the threshold for transition to turbulence for plane Poiseuille flow 15:15 15 mins #622 Wave focusing and multiple dispersion transitions of perturbation waves in the plane Poiseuille flow Gabriele Nastro, Federico Fraternale, Daniela Tordella Abstract: We investigated the capacity of parallel flows to host both dispersive and non-dispersive small perturbation waves under fixed flow conditions [1, 2]. Although it is known that long perturbation waves may slowly disperse [3,4,5], this scenario is not yet complete. For the plane Poiseuille flow, by computing the dispersion relation of perturbations observed in their long-term, we show that wave dispersion does not occur at all wavenumbers k and in the whole range of Reynolds number R. In fact, for a fixed value of R, waves with a shorter length than a specific threshold propagate non-dispersively, as shown in [1] and in Figure 1(a). The present study extends these results and considers the impact on three-dimensional localized disturbances. By finely tuning the wavenumber and Reynolds number resolution, we explored the stability map in the limit of long waves. We discovered the existence of three regions of the parameters space, having different dispersion features than their surroundings. In particular, these regions look like niches tilted by 45 degrees in the log-log space, which are nested in the dispersive part of the map. The first one is observed at R larger than 546 and k below 0.28, and shows a higher propagation speed than the surroundings, associated with a mild dispersion. The second is observed for R larger than 9770 and k below 0.13, and highlights again a larger propagation speed than the surroundings and but an enhanced dispersion. The last one is observed for R larger than 29840 and k below 0.35, and contains non-dispersive waves that propagate with the convective speed of the basic flow. The wave packet morphology has been then related to the scattering properties of the wave components inside the packet. In particular, the front of the linear spot [6] - also present in pipe puffs [7] - appears associated with the non-dispersive components. This helps to understand the physical mechanisms determining the spot arrow-shape and spatial spreading of the spot, an aspect still missing in the literature [8, 9]. With the help of a propagation representation, based on the directional distribution of the computed asymptotic group velocity, we qualitatively reconstruct the features of the spot, see Figure 1(b,c). References [1] F. De Santi, F. Fraternale, and D. Tordella. Dispersive-to-nondispersive transition and phase-velocity transient for linear waves in plane wake and channel flows. Phys. Rev. E, 93(3), 2016. [2] F. Fraternale, L. Domenicale, G. Staffilani, and D. Tordella. Internal waves in sheared flows: Lower bound of the vorticity growth and propagation discontinuities in the parameter space. Phys. Rev. E, 97(6), 2018. [3] W. O. Criminale and L. S. G. Kovasznay. The growth of localized disturbances in a laminar boundary layer. J. Fluid Mech., 14(1):59–80, 1962. [4] M. Gaster. The development of three-dimensional wave packets in a boundary layer. J. Fluid Mech., 32(1):173–184, 1968. [5] M. Gaster. Propagation of linear wave packets in laminar boundary layers. AIAA J., 19(4):419–423, 1981. [6] M. T. Landahl. Wave mechanics of breakdown. J. Fluid Mech., 56(28):775–802, 1972. [7] P. Manneville. Transition to turbulence in wall-bounded flows: Where do we stand? Mech. Eng. Rev., 3(2):15–00684–15–00684, 2016. [8] D. S. Henningson, Johansson A. V., and P. H. Alfredsson. Turbulent spots in channel flows. J. Eng. Math., 28(1):21–42, 1994. [9] G. Lemoult, K. Gumowski, J-L. Aider, and J. E. Wesfreid. Turbulent spots in channel flow: An experimental study. Eur. Phys. J. E, 37(4):1–11, 2014. 15:30 15 mins #300 Nonlinear dynamics of bursting spots in subcritical inclined convection Florian Reetz, Tobias M. Schneider Abstract: Thermal convection in a fluid layer which is strongly inclined against gravity may give rise to spatially localized bursts of intense convection within a background of weak streamwise oriented convection rolls. These spots are observed slightly above the critical linear threshold for onset of convection [1]. Despite the fact that bursting spots emerge close to linear thresholds, linear or weakly nonlinear theory cannot explain their dynamics. The bursting dynamics and the spatial localization of these spots require a fully nonlinear approach. We numerically identified fully nonlinear exact coherent states in inclined layer convection (ILC) at Pr = 1.07 and inclination angle γ = 77◦ that clearly resemble the localized pattern of bursting spots (Figure 1). These exact equilibrium and traveling wave solutions are weakly unstable and exist at parameters where laminar ILC is linearly stable and a spatial coexistence of exact coherent states is possible. We explain how exact spot solutions bifurcate from straight convection rolls, and discuss conditions for observing the formation of bursting spots in subcritical ILC.