Related papers: On the resolvent technique for stability of plane …
We present an equilibrium solution of plane Couette flow that is exponentially localized in both the spanwise and streamwise directions. The solution is similar in size and structure to previously computed turbulent spots and localized,…
Threshold amplitude of disturbance for transition to turbulence in a pipe Poiseuille flow is investigated. Based on the energy gradient theory, we argued that the transition to turbulence depends on magnitudes of the energy gradient of mean…
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…
This paper provides a pedagogical introduction to the classical nonlinear stability analysis of the plane Poiseuille and Couette flows. The whole procedure is kept as simple as possible by presenting all the logical steps involved in the…
The relation between rotating plane Couette and Taylor-Couette flows is clarified. The identity of their linear stability limits is explained by considering the effect of the Coriolis force in the rotating frame. Experimental data are used…
Variational turbulence is among the few approaches providing rigorous results in turbulence. In addition, it addresses a question of direct practical interest, namely the rate of energy dissipation. Unfortunately, only an upper bound is…
Extreme Value Theory (EVT) is exploited to determine the global stability threshold $R_g$ of plane Couette flow --the flow of a viscous fluid in the space between two parallel plates-- whose laminar or turbulent behavior depends on the…
In this paper, we study the linear stability of Couette flow for 2D compressible Navier-Stokes-Poisson system at high Reynolds number in the domain $\mathbb{T}\times\mathbb{R}$ with initial perturbation in Sobolev spaces. We establish the…
In this paper, we investigate the nonlinear stability of the Couette flow for the two-dimensional compressible Navier--Stokes equations at high Reynolds numbers ($Re$) regime. It was proved that if the initial data $(\rho_{in},u_{in})$…
Direct numerical simulations have proven of inestimable help to our understanding of the transition to turbulence in wall-bounded flows. While the dynamics of the transition from laminar flow to turbulence via localised spots can be…
We present an experimental study of transition to turbulence in a plane Poiseuille flow. Using a well-controlled perturbation, we analyse the flow using extensive Particule Image Velocimetry and flow visualisation (using Laser Induced…
We present a unique method for solving for the Reynolds stress in turbulent canonical flows, based on the momentum balance for a control volume moving at the local mean velocity. A differential transform converts this momentum balance to a…
A novel method to estimate unsteady aerodynamic force coefficients from pointwise velocity measurements is presented. The methodology is based on a resolvent-based reduced-order model which requires the mean flow to obtain physical flow…
The normal-mode analysis of the Reynolds-Orr energy equation governing the stability of viscous motion for general three-dimensional disturbances has been revisited. The energy equation has been solved as an unconstrained minimization…
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…
Transition to turbulence dramatically alters the properties of fluid flows. In most canonical shear flows, the laminar flow is linearly stable and a finite-amplitude perturbation is necessary to trigger transition. Controlling transition to…
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 ultimate goal of a sound theory of turbulence in fluids is to close in a rational way the Reynolds equations, namely to express the time averaged turbulent stress tensor as a function of the time averaged velocity field. This closure…
This article presents direct numerical simulations of the growth of turbulent spots in the transitional regime of plane Couette flow. A quantitative description of the growth process and of the detail of the quadrupolar flow around the spot…
A novel turbulence control strategy for wall-bounded shear flow is proposed by Chagelishvili et al, 2014. The essence of this strategy involves continuously imposition of specially designed seed velocity perturbations with spanwise…