Related papers: From temporal to spatiotemporal dynamics in transi…
Using a reduced model focusing on the in-plane dependence of plane Couette flow, it is shown that the turbulent-to-laminar relaxation process can be understood as a nucleation problem similar to that occurring at a thermodynamic first-order…
Plane Couette flow, the flow between two parallel planes moving in opposite directions, is an example of wall-bounded flow experiencing a transition to turbulence with an ordered coexistence of turbulent and laminar domains in some range of…
In wide enough systems, plane Couette flow, the flow established between two parallel plates translating in opposite directions, displays alternatively turbulent and laminar oblique bands in a given range of Reynolds numbers R. We show that…
The transition mechanism from laminar flow to turbulent flow is a central problem in hydrodynamic stability theory. To shed light on this transition mechanism, Trefethen et al.({\it \small Science 1993}) proposed the transition threshold…
Upon decreasing the Reynolds number, plane Couette flow first forms alternately turbulent and laminar oblique bands out of featureless turbulence below some upper threshold R_t. These bands exist down to a global stability threshold R_g…
In this essay, we recall the specificities of the transition to turbulence in wall-bounded flows and present recent achievements in the understanding of this problem. The transition is abrupt with laminar-turbulent coexistence over a finite…
Contrasting with free shear flows presenting velocity profiles with inflection points which cascade to turbulence in a relatively mild way, wall bounded flows are deprived of (inertial) instability modes at low Reynolds numbers and become…
The decay of turbulent and laminar oblique bands in the lower transitional range of plane Couette flow is studied by means of direct numerical simulations of the Navier--Stokes equations. We consider systems that are extended enough for…
In wall-bounded flows, the laminar regime remain linearly stable up to large values of the Reynolds number while competing with nonlinear turbulent solutions issued from finite amplitude perturbations. The transition to turbulence of plane…
The transitional regime of plane channel flow is investigated {above} the transitional point below which turbulence is not sustained, using direct numerical simulation in large domains. Statistics of laminar-turbulent spatio-temporal…
Low Reynolds number turbulence in wall-bounded shear flows \emph{en route} to laminar flow takes the form of oblique, spatially-intermittent turbulent structures. In plane Couette flow, these emerge from uniform turbulence via a…
Intermittent turbulent-laminar patterns characterize the transition to turbulence in pipe, plane Couette and plane channel flows. The time evolution of turbulent-laminar bands in plane channel flow is studied via direct numerical…
Abrupt transition to turbulence may occur in pipe and channel flows at moderate flow rates, an unexpected event according to linear stability theory, and has been an open problem in fluid dynamics for more than a century. Extensive…
Wall-bounded flows experience a transition to turbulence characterized by the coexistence of laminar and turbulent domains in some range of Reynolds number R, the natural control parameter. This transitional regime takes place between an…
A central obstacle to understanding the route to turbulence in wall-bounded flows is that the flows are composed of complex, highly fluctuating, and strongly nonlinear states. In the case of pipe flow, models have deepened our understanding…
A turbulent-laminar banded pattern in plane Couette flow is studied numerically. This pattern is statistically steady, is oriented obliquely to the streamwise direction, and has a very large wavelength relative to the gap. The mean flow,…
This article presents the finite size analysis of two consecutive crossovers leading laminar-turbulent bands to uniform wall turbulence in transitional plane Couette flow. Direct numerical simulations and low order modeling simulations of…
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…
Plane Couette flow presents a regular oblique turbulent-laminar pattern over a wide range of Reynolds numbers R between the globally stable base flow profile at low R<R_g and a uniformly turbulent regime at sufficiently large R>R_t. The…
Spatially localized states play an important role in transition to turbulence in shear flows (Kawahara, Uhlmann & van Veen, Annu. Rev. Fluid Mech. 44, 203 (2012)). Despite the fact that some of them are attractors on the separatrix between…