Formation of turbulent patterns near the onset of transition in plane Couette flow

Abstract

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 Rec = 324 ± 1. For Rec < Re ≤ 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.

Turbulent bands in plane-Poiseuille flow at moderate Reynolds numbers

“…Unlike the PPF, the basic state of PCF has velocities in opposite directions on each channel half, and hence, the perturbations extend in a zigzag style. 25 When the band is long enough, its two ends are close to each other due to the periodic boundary conditions, and the interactions between the large-scale flows around the ITBs cause band breaking as reported in Fig. 2(e).…”

“…The mechanism for the growth in the oblique direction is similar to that of PCF, [24][25][26] where the large-scale motions play the key role. At t = 950, a long band is formed (see Fig.…”

“…Similarly, a simulation of plane-Couette flow showed that the turbulent fraction did not converge to a statistically steady value at Re = 325. 25 In this letter, we used more samples to study the long-term effect of band interaction on the volume-averaged kinetic energy of the whole flow field. A flow state similar to that depicted in Fig.…”

A statistical mechanical phase transition to turbulence in a model shear flow

“…The size of the flow domain is very important to capture the necessary phenomena, because of the huge separation of time scales that emerges near the transition. To date, the state-of-the-art was the plane Couette simulations of Duguet, Schlatter & Henningson (2010), conducted in a spatial domain whose [x, y, z] dimensions were [800h, 2h, 356h] where 2h is the gap between the walls, and which lasted O(10 4 ) time units. In contrast, the study of Chantry et al (2017) was in a computational domain of streamwise and spanwise size 2560h × 2560h, and lasted O(10 6 ) time units; thus it was not simply an incremental improvement on the state-of-the-art.…”

Doubly localized states in plane Couette flow

“…It should be promising to follow them through their bifurcations to also reach upper branch states around which longer-lived turbulent dynamics can be observed. It should then be interesting and rewarding to relate the properties of these localized states to the patterns seen by Barkley & Tuckerman (2005) and the correlation properties of the spatiotemporal patterns described in Duguet et al (2010).…”