Related papers: Nonlinear stability analysis of plane Poiseuille f…
In this paper, we study the stability for 2-D plane Poiseuille flow $(1-y^2,0)$ in a channel $\mathbb{T}\times (-1,1)$ with Navier-slip boundary condition. We prove that if the initial perturbation for velocity field $u_0$ satisfies that…
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…
We study the stability of plane Poiseuille flow (PPF) and plane Couette flow (PCF) subject to streamwise system rotation using linear stability analysis and direct numerical simulations. The linear stability analysis reveals two asymptotic…
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 $(\rho_{in},u_{in})$…
We study the nonlinear stability of plane Couette and Poiseuille flows with the Lyapunov second method by using the classical L2-energy. We prove that the streamwise perturbations are L2-energy stable for any Reynolds number. This…
We perform a detailed numerical study of modal and non-modal stability in oblique Couette-Poiseuille profiles, which are among the simplest examples of three-dimensional boundary layers. Through a comparison with the Orr-Sommerfeld operator…
The paper considers a two-dimensional flow in a channel, which consists of straight inlet and outlet branches and a circularly 90-degree curved bend. An incompressible viscous fluid flows through the elbow under the action of a constant…
The paper examines the issue of stability of Poiseuille type flows in regime of compressible Navier-Stokes equations in a three dimensional finite pipe-like domain. We prove the existence of stationary solutions with inhomogeneous Navier…
We study the effect of the Reynolds number on the flow of a generalized Newtonian fluid through a thin porous medium in $\mathbb{R}^3$. This medium is a domain of thickness $\varepsilon \ll 1$, perforated by periodically distributed solid…
We characterize the behavior of stochastic Navier-Stokes on $\mathbb{T} \times [-1,1]$ with Navier boundary conditions at high Reynolds number when initialized near Couette flow subject to small additive stochastic forcing. We take additive…
Channel flow is usually described by Darcy law with the Poiseuille flow profile. However, for incompressible channel flow there is a critical state, characterized by a critical Reynolds number $Re_c$ and a critical wavevector mc, beyond…
Reduced-order models were derived for plane Couette flow using Galerkin projection, with orthonormal basis functions taken as the leading controllability modes of the linearised Navier-Stokes system for a few low wavenumbers. Resulting…
Plane Poiseuille flow shows turbulence at a Reynolds number that is lower than the critical one for the onset of Tollmien-Schlichting waves. The transition to turbulence follows the same route as the by-pass transition in boundary layers,…
We investigate here linear stability in a canonical three-dimensional boundary layer generated by the superposition of a spanwise pressure gradient upon an otherwise standard channel flow. As the main result, we introduce a simple…
Critical Reynolds numbers for the monotone exponential energy stability of Couette and Poiseuille plane flows were obtained by Orr 1907 \cite{Orr1907} in a famous paper, and by Joseph 1966 \cite{Joseph1966}, Joseph and Carmi 1969…
The transition to turbulence in plane Poiseuille flow (PPF) is connected with the presence of exact coherent structures. In contrast to other shear flows, PPF has a number of different coherent states that are relevant for the transition.…
Laminar flows through pipes driven at steady, pulsatile or oscillatory rates undergo a sub-critical transition to turbulence. We carry out an extensive linear non-modal stability analysis of these flows and show that for sufficiently high…
Experiments (Mullin and Kreswell, 2005) show that transition to turbulence can start at Reynolds numbers lower than it is predicted by the linear stability analysis - the subcritical transition to turbulence. To explain these observations…
This paper concerns the Couette flow for 2-D compressible Navier-Stokes equations (N-S) in an infinitely long flat torus $\Torus\times\R$. Compared to the incompressible flow, the compressible Couette flow has a stronger lift-up effect and…
Subject of this paper falls under the broad heading of the propagation of disturbances causing transition in a fully developed spiral annular flow. The problem is approached through reformulation of the linearised equations of motion…