Relative periodic edge orbits in plane channel flow

A branch of genuine relative periodic orbits is found to be an edge state in plane Poiseuille flow in a periodic domain. These periodic solutions correspond to sinuous quasi-streamwise streaks periodically forced by sinuous quasi streamwise vortices in a self-sustained process. The rms-amplitude of the streaks is found to scale as ≈ Re-0.8, while that of the quasi-streamwise vortices scales like ≈ Re-1.6

On the self-sustained nature of large-scale motions in turbulent Couette flow

Large-scale motions in wall-bounded turbulent flows are frequently interpreted as resulting from an aggregation process of smaller-scale structures. Here, we explore the alternative possibility that such large-scale motions are themselves self-sustained and do not draw their energy from smaller-scale turbulent motions activated in buffer layers. To this end, it is first shown that large-scale motions in turbulent Couette flow at Re=2150 self-sustain even when active processes at smaller scales are artificially quenched by increasing the Smagorinsky constant Cs in large eddy simulations. These results are in agreement with earlier results on pressure driven turbulent channels. We further investigate the nature of the large-scale coherent motions by computing upper and lower-branch nonlinear steady solutions of the filtered (LES) equations with a Newton-Krylov solver,and find that they are connected by a saddle-node bifurcation at large values of Cs. Upper branch solutions for the filtered large scale motions are computed for Reynolds numbers up to Re=2187 using specific paths in the Re-Cs parameter plane and compared to large-scale coherent motions. Continuation to Cs = 0 reveals that these large-scale steady solutions of the filtered equations are connected to the Nagata-Clever-Busse-Waleffe branch of steady solutions of the Navier-Stokes equations. In contrast, we find it impossible to connect the latter to buffer layer motions through a continuation to higher Reynolds numbers in minimal flow units

Coherent dynamics of large scale turbulent motions

My thesis work focused on ‘dynamical systems’ understanding of the large-scale dynamics in fully developed turbulent shear flow. In plane Couette flow, large-eddy simulation (L.E.S) is used to model small scale motions and to only resolve large-scale motions in order to compute nonlinear traveling waves (NTW) and relative periodic orbits (RPO). Artificial over-damping has been used to quench an increasing range of small-scale motions and prove that the motions in large-scale are self-sustained. The lower-branch traveling wave solutions that lie on laminar-turbulent basin boundary are obtained for these over-damped simulation and further continued in parameter space to upper branch solutions. This approach would not have been possible if, as conjectured in some previous investigations, large-scale motions in wall bounded shear flows are forced by mechanism based on the existence of active structures at smaller scales. In Poseuille flow, relative periodic orbits with shift-reflection symmetry on the laminar-turbulent basin boundary are computed using DNS. We show that the found RPO are connected to the pair of traveling wave (TW) solution via global bifurcation (saddle-node-infinite period bifurcation). The lower branch of this TW solution evolve into a spanwise localized state when the spanwise domain is increased. The upper branch solution develops multiple streaks with spanwise spacing consistent with large-scale motions in turbulent regime

Dynamique cohérente de mouvements turbulents à grande échelle

Mon travail de thèse a porté sur la compréhension «systèmes dynamiques de la dynamique à grande échelle dans l’écoulement pleinement développé de cisaillement turbulent. Dans le plan écoulement de Couette, simulation des grandes échelles (LES) est utilisée pour modéliser petits mouvements d’échelle et de ne résoudre mouvements à grande échelle afin de calculer non linéaire ondes progressives (SNT) et orbites périodiques relatives (RPO). Artificiel sur-amortissement a été utilisé pour étancher une gamme croissante de petite échelle motions et prouvent que les motions grande échelle sont auto-entretenue. Les solutions d’onde inférieure branche itinérantes qui se trouvent sur le bassin laminaire turbulent limite sont obtenues pour ces simulation sur-amortie et continue encore dans l’espace de paramètre à des solutions de branche supérieure. Cette approche ne aurait pas été possible si, comme supposé dans certains enquêtes précédentes, les mouvements à grande échelle dans le mur bornées flux de cisaillement sont forcée par un mécanisme fondé sur l’existence de structures actives à plus petite échelle. En flux Poseuille, orbites périodiques relatives à décalage réflexion symétrie sur la limite du bassin laminaire turbulent sont calculés en utilisant DNS. Nous montrons que le RPO trouvé sont connectés à la paire de voyager vague (TW) solution via bifurcation mondiale (noeud-col-période infinie bifurcation). La branche inférieure de cette solution TW évoluer dans un état de l’envergure localisée lorsque le domaine de l’envergure est augmentée. La solution de branche supérieure développe plusieurs stries avec un espacement de l’envergure compatible avec des mouvements à grande échelle en régime turbulent. ABSTRACT : My thesis work focused on ‘dynamical systems’ understanding of the large-scale dynamics in fully developed turbulent shear flow. In plane Couette flow, large-eddy simulation (L.E.S) is used to model small scale motions and to only resolve large-scale motions in order to compute nonlinear traveling waves (NTW) and relative periodic orbits (RPO). Artificial over-damping has been used to quench an increasing range of small-scale motions and prove that the motions in large-scale are self-sustained. The lower-branch traveling wave solutions that lie on laminar-turbulent basin boundary are obtained for these over-damped simulation and further continued in parameter space to upper branch solutions. This approach would not have been possible if, as conjectured in some previous investigations, large-scale motions in wall bounded shear flows are forced by mechanism based on the existence of active structures at smaller scales. In Poseuille flow, relative periodic orbits with shift-reflection symmetry on the laminar-turbulent basin boundary are computed using DNS. We show that the found RPO are connected to the pair of traveling wave (TW) solution via global bifurcation (saddle-node-infinite period bifurcation). The lower branch of this TW solution evolve into a spanwise localized state when the spanwise domain is increased. The upper branch solution develops multiple streaks with spanwise spacing consistent with large-scale motions in turbulent regime

Relative periodic orbits in plane Poiseuille flow

A branch of relative periodic orbits is found in plane Poiseuille flow in a periodic domain at Reynolds numbers ranging from Re = 3000 to Re = 5000. These solutions consist in sinuous quasi-streamwise streaks periodically forced by quasi-streamwise vortices in a self-sustained process. The streaks and the vortices are located in the bulk of the flow. Only the amplitude, but not the shape, of the averaged velocity components does change as the Reynolds number is increased from 3000 to 5000. We conjecture that these solutions could therefore be related to large- and very large-scale structures observed in the bulk of fully developed turbulent channel flows

Travelling-wave solutions bifurcating from relative periodic orbits in plane Poiseuille flow

Travelling-wave solutions are shown to bifurcate from relative periodic orbits in plane Poiseuille flow at Re = 2000 in a saddle-node infinite-period bifurcation. These solutions consist in self-sustaining sinuous quasi-streamwise streaks and quasi-streamwise vortices located in the bulk of the flow. The lower branch travelling-wave solutions evolve into spanwise localized states when the spanwise size L z of the domain in which they are computed is increased. On the contrary, the upper branch of travelling-wave solutions develops multiple streaks when L z is increased. Upper-branch travelling-wave solutions can be continued into coherent solutions to the filtered equations used in large-eddy simulations where they represent turbulent coherent large-scale motions

Drag modulation in turbulent boundary layers subject to different bubble injection strategies

The aim of this study is to investigate numerically the interaction between a dispersed phase composed of micro-bubbles and a turbulent boundary layer flow. We use the Euler–Lagrange approach based on Direct Numerical Simulation of the continuous phase flow equations and a Lagrangian tracking for the dispersed phase. The Synthetic Eddy Method (SEM) is used to generate the inlet boundary condition for the simulation of the turbulent boundary layer. Each bubble trajectory is calculated by integrating the force balance equation accounting for buoyancy, drag, added-mass, pressure gradient, and the lift forces. The numerical method accounts for the feedback effect of the dispersed bubbles on the carrying flow. Our approach is based on local volume average of the two-phase Navier–Stokes equations. Local and temporal variations of the bubble concentration and momentum source terms are accounted for in mass and momentum balance equations. To study the mechanisms implied in the modulation of the turbulent wall structures by the dispersed phase, we first consider simulations of the minimal flow unit laden with bubbles. We observe that the bubble effect in both mass and momentum equations plays a leading role in the modification of the flow structures in the near wall layer, which in return generates a significant increase of bubble volume fraction near the wall. Based on these findings, we discussed the influence of bubble injection methods on the modulation of the wall shear stress of a turbulent boundary layer on a flat plate. Even for a relatively small bubble volume fraction injected in the near wall region, we observed a modulation in the flow dynamics as well as a reduction of the skin friction

Coherent dynamics of large scale turbulent motions

Mon travail de thèse a porté sur la compréhension «systèmes dynamiques de la dynamique à grande échelle dans l’écoulement pleinement développé de cisaillement turbulent. Dans le plan écoulement de Couette, simulation des grandes échelles (LES) est utilisée pour modéliser petits mouvements d’échelle et de ne résoudre mouvements à grande échelle afin de calculer non linéaire ondes progressives (SNT) et orbites périodiques relatives (RPO). Artificiel sur-amortissement a été utilisé pour étancher une gamme croissante de petite échelle motions et prouvent que les motions grande échelle sont auto-entretenue. Les solutions d’onde inférieure branche itinérantes qui se trouvent sur le bassin laminaire turbulent limite sont obtenues pour ces simulation sur-amortie et continue encore dans l’espace de paramètre à des solutions de branche supérieure. Cette approche ne aurait pas été possible si, comme supposé dans certains enquêtes précédentes, les mouvements à grande échelle dans le mur bornées flux de cisaillement sont forcée par un mécanisme fondé sur l’existence de structures actives à plus petite échelle. En flux Poseuille, orbites périodiques relatives à décalage réflexion symétrie sur la limite du bassin laminaire turbulent sont calculés en utilisant DNS. Nous montrons que le RPO trouvé sont connectés à la paire de voyager vague (TW) solution via bifurcation mondiale (noeud-col-période infinie bifurcation). La branche inférieure de cette solution TW évoluer dans un état de l’envergure localisée lorsque le domaine de l’envergure est augmentée. La solution de branche supérieure développe plusieurs stries avec un espacement de l’envergure compatible avec des mouvements à grande échelle en régime turbulent.My thesis work focused on ‘dynamical systems’ understanding of the large-scale dynamics in fully developed turbulent shear flow. In plane Couette flow, large-eddy simulation (L.E.S) is used to model small scale motions and to only resolve large-scale motions in order to compute nonlinear traveling waves (NTW) and relative periodic orbits (RPO). Artificial over-damping has been used to quench an increasing range of small-scale motions and prove that the motions in large-scale are self-sustained. The lower-branch traveling wave solutions that lie on laminar-turbulent basin boundary are obtained for these over-damped simulation and further continued in parameter space to upper branch solutions. This approach would not have been possible if, as conjectured in some previous investigations, large-scale motions in wall bounded shear flows are forced by mechanism based on the existence of active structures at smaller scales. In Poseuille flow, relative periodic orbits with shift-reflection symmetry on the laminar-turbulent basin boundary are computed using DNS. We show that the found RPO are connected to the pair of traveling wave (TW) solution via global bifurcation (saddle-node-infinite period bifurcation). The lower branch of this TW solution evolve into a spanwise localized state when the spanwise domain is increased. The upper branch solution develops multiple streaks with spanwise spacing consistent with large-scale motions in turbulent regime

Relative periodic edge orbits in plane channel flow

International audienceA branch of genuine relative periodic orbits is found to be an edge state in plane Poiseuille flow in a periodic domain. These periodic solutions correspond to sinuous quasi-streamwise streaks periodically forced by sinuous quasi streamwise vortices in a self-sustained process. The rms-amplitude of the streaks is found to scale as ≈ Re-0.8, while that of the quasi-streamwise vortices scales like ≈ Re-1.6

Exact Invariant Solutions for Coherent Turbulent Motions in Couette and Poiseuille Flows

International audienceThe dynamical systems approach recently applied to understand subcritical transitions in wall-bounded shear flows is combined with the use of large-eddy simulations to investigate the nature of large-scale coherent motions in turbulent Couette and Poiseuille flows. Exact invariant solutions of the filtered Navier-Stokes (LES) equations are computed by using the Smagorinsky model to parametrize small-scale motions. These solutions can be continued into exact solutions of the Navier-Stokes equations, therefore providing a bridge between coherent large-scale motions in wall-bounded fully developed turbulent flows and invariant solutions appearing in transitional flows