Large scale flow around turbulent spots

Fluid Mechanics and its Applications

Regular patterns of turbulent and laminar fluid motion arise in plane Couette flow near the lowest Reynolds number for which turbulence can be sustained. We study these patterns using an extension of the minimal flow unit approach to simulations of channel flows pioneered by Jiménez and Moin. In our case computational domains are of minimal size in only two directions. The third direction is taken to be large. Furthermore, the long direction can be tilted at any prescribed angle to the streamwise direction. We report on different patterned states observed as a function of Reynolds number, imposed tilt, and length of the long direction. We compare our findings to observations in large aspect-ratio experiments.

Journal of Fluid Mechanics, 2010

The formation of turbulent patterns in plane Couette flow is investigated near the onset of transition, using numerical simulation in a very large domain of size 800 h × 2 h × 356 h. Based on a maximum observation time of 20 000 inertial units, the threshold for the appearance of sustained turbulent motion is Re c = 324 ± 1. For Re c < Re 6 380, turbulent-banded patterns form, irrespective of whether the initial perturbation is a noise or localized disturbance. Measurements of the turbulent fraction versus Re show evidence for a discontinuous phase transition scenario where turbulent spots play the role of the nuclei. Using a smaller computational box, the angle selection of the turbulent bands in the early stages of their development is shown to be related to the amplitude of the initial perturbation.

2016

Isolating turbulent spots in stratified Plane-Couette flow John R. Taylor 1 , Enrico Deusebio, Colm-cille Caulfield 2,1 and Rich Kerswell 3 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Willberforce Road, CB3 0WA, Cambridge BP Institute, University of Cambridge, Madingley Road, CB3 0EZ, Cambridge School of Mathematics, University of Bristol, BS8 1TW, Bristol Abstract We present a new adaptive control strategy to isolate and stabilize turbulent states in intermittent stably-stratified plane Couette flow in which the gravitational acceleration (non-dimensionalized as the bulk Richardson number Ri) is adjusted in time to maintain the turbulent kinetic energy (TKE) of the flow. We demonstrate that applying this method at various stages of decaying stratified turbulence halts the decay process and allows a succession of intermediate turbulent states of decreasing energy to be isolated and stabilized. Once the energy ...

Journal of Fluid Mechanics, 2021

In this paper we experimentally study the transitional range of Reynolds numbers in plane Couette-Poiseuille flow, focusing our attention on the localized turbulent structures triggered by a strong impulsive jet and the large-scale flow generated around these structures. We present a detailed investigation of the large-scale flow and show how its amplitude depends on Reynolds number and amplitude perturbation. In addition, we characterize the initial dynamics of the localized turbulent spot, which includes the coupling between the small and large scales, as well as the dependence of the advection speed on the large-scale flow generated around the spot. Finally, we provide the first experimental measurements of the large-scale flow around an oblique turbulent band.

Physical Review E, 2011

Laboratory experiments point out the existence of patterns made of alternately laminar and turbulent oblique bands in plane Couette flow in its way to/from turbulence as the Reynolds number R is varied. Many previous theoretical and numerical works on the problem have considered small aspect-ratio systems subjected to periodic boundary conditions, while experiments correspond to the opposite limit of large aspect-ratio. Here, by means of fully resolved direct numerical simulations of the Navier-Stokes equations at decreasing R, we scrutinize the transition from temporal to spatiotemporal behavior in systems of intermediate sizes. We show that there exists a streamwise crossover size of order L x ∼70-80 h (where 2h is the gap between the plates driving the flow) beyond which the transition to/from turbulence in PCF is undoubtedly a spatiotemporal process, with typical scenario '[turbulent flow] → [riddled regime] → [oblique pattern] → [laminar flow]', whereas below that size it is more a temporal process describable in terms of finite-dimensional dynamical systems with scenario '[chaotic flow] → [laminar flow]' (via chaotic transients). In the crossover region, the '[oblique pattern]' stage is skipped, which leads us to suggest that an appropriate rendering of the patterns observed in experiments needs a faithful account of streamwise correlations at scales at least of the order of that crossover size.

Physical Review Letters, 2005

Turbulent-laminar patterns near transition are simulated in plane Couette flow using an extension of the minimal flow unit methodology. Computational domains are of minimal size in two directions but large in the third. The long direction can be tilted at any prescribed angle to the streamwise direction. Three types of patterned states are found and studied: periodic, localized, and intermittent. These correspond closely to observations in large aspect ratio experiments.

Physics of Fluids, 2015

Using Particle Image Velocimetry (PIV) in a new experimental plane Couette flow, we investigate the dynamics of turbulent patches invading formerly laminar flows. We evidence experimentally for the first time in this geometry the existence of large scale flows. These flows appear as soon as laminar and turbulent domains coexist. Spectral analysis is used to study the dynamical evolution of these large scales as well as that of the small scales associated with turbulence. We show that large-scale flows grow before turbulent spots develop and we point out the crucial role they play in the growth mechanism and possibly also in the emergence of organised patterns.

Fluid Dynamics Research, 2012

The growth of laminar-turbulent band patterns in plane Couette flow is studied in the vicinity of the global stability threshold Re g below which laminar flow ultimately prevails. Appropriately tailored direct numerical simulations are performed to manage systems extended enough to accommodate several bands. The initial state or germ is an oblique turbulent patch of limited extent. The growth is seen to result from several competing processes: (i) nucleation of turbulent patches close to or at the extremities of already formed band segments, with the same obliquity as the germ or the opposite one, and (ii) turbulence collapse similar to gap formation for band decay. Growth into a labyrinthine pattern is observed as soon as spanwise expansion is effective. An ideally aligned pattern is usually obtained at the end of a long and gradual regularisation stage when Re is large enough. Stable isolated bands can be observed slightly above Re g. When growth rates are not large enough, the germ decays at the end of a long transient, similar to what was observed in experiments. Local continuous growth/decay microscopic mechanisms are seen to compete with large deviations which are the cause of mesoscopic nucleation events (turbulent patches or laminar gaps) controlling the macroscopic behaviour of the system (pattern). Implications of these findings are discussed in the light of Pomeau's proposals based on directed percolation and first-order phase transitions in statistical physics.

Journal of Fluid Mechanics, 2017

We present detailed experiments on transient growth of turbulent spots induced by external forcing in plane Couette–Poiseuille flow, which are studied in the framework of linear transient growth. The experimental investigation is supplemented with full theoretical analysis. We compare quantitatively the experimental and theoretical results, including maximal gain and the time at which it occurs. We also present the limits of validity for the application of the linear theory at high amplitude perturbation and Reynolds number, showing experiments with self-sustained states.

Experiments in Fluids, 2003

Experimental results are presented on the transition to turbulence of a plane Couette flow locally and permanently forced by a small bead. The intermittent aspect of this transition is investigated in a detailed analysis of the transition periods from coherent to turbulent and vice versa. A maximum number of transitions are achieved at a Reynolds number of about 310. It is shown that the breakdown of the flow coherence results from a complex succession of events occurring as follows. A secondary instability takes place leading to a drift of at least one vortex pair away from the excitation source. Consequently, the flow in the bead vicinity is laminar and a vortex pair is generated. Turbulence results from the interaction between the newly born vortex and the one already active. As the fluctuation intensity decreases all over the flow, the laminar state is recovered in the bead vicinity from which two vortex pairs are regenerated. The second main contribution of this paper is the study of the turbulent state using spatio-temporal correlation. The role of lateral streaks and their properties in the turbulent state are investigated. It is demonstrated that the turbulent spot is sustained by a vortex generation near the source followed by convection towards the boundaries. In both coherent and turbulent states, the flow near the bead is found to determine the plane Couette flow evolution.