Related papers: Improved global stability bounds for two-dimension…
Verifying nonlinear stability of a laminar fluid flow against all perturbations is a central challenge in fluid dynamics. Past results rely on monotonic decrease of a perturbation energy or a similar quadratic generalized energy. None show…
In this article we prove, choosing an appropriately weighted $L_2$-energy equivalent to the classical energy, that the plane Couette and Poiseuille flows are nonlinearly stable with respect to streamwise perturbations for any Reynolds…
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…
The linear evolution of disturbances due to a ribbon vibrating at frequency $\omega_0$ in plane Poiseuille flow is computed by solving the associated initial boundary value problem in the Fourier-Laplace plane, followed by inversion. A…
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…
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…
In the subcritical interval of the Reynolds number 4320\leq R\leq R_c\equiv 5772, the Navier--Stokes equations of the two--dimensional plane Poiseuille flow are approximated by a 22--dimensional Galerkin representation formed from…
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…
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 energy method, also known as the Reynolds-Orr equation, is widely utilized in predicting the unconditional stability threshold of shear flows owing to the zero contribution of nonlinear terms to the time derivative of perturbation…
In this paper, we study the nonlinear stability for the 3-D plane Poiseuille flow $(1-y^2,0,0)$ at high Reynolds number $Re$ in a finite channel $\mathbb{T}\times [-1,1 ]\times \mathbb{T}$ with non-slip boundary condition. We prove that if…
We show possibility of the Plane Couette (PC) flow instability for Reynolds number Re>Reth=140. This new result of the linear hydrodynamic stability theory is obtained on the base of refusal from the traditionally used assumption on…
The stability of plane Poiseuille flow of a viscous Newtonian fluid in a multilayer channel with anisotropic porous walls is analyzed using the classical modal analysis, the energy method, and the non-modal analysis. The influence of porous…
For applications regarding transition prediction, wing design and control of boundary layers, the fundamental understanding of disturbance growth in the flat-plate boundary layer is an important issue. In the present work we investigate the…
We present a detailed study of the linear stability of plane Couette-Poiseuille flow in the presence of a cross-flow. The base flow is characterised by the cross flow Reynolds number, $R_{inj}$ and the dimensionless wall velocity, $k$.…
A modal stability analysis shows that plane Poiseuille flow of an Oldroyd-B fluid becomes unstable to a `center mode' with phase speed close to the maximum base-flow velocity, $U_{max}$. The governing dimensionless groups are the Reynolds…
We study the monotone energy stability of ``Poiseuille flow" in a plane-parallel channel with a saturated porous medium modeled by the Brinkman equation, on the basis of an analogy with a magneto-hydrodynamic problem (Hartmann flow) (cf.…
In this study we consider the stability and transitions for the Poiseuille flow of a second grade fluid which is a model for non-Newtonian fluids. We restrict our attention to flows in an infinite pipe with circular cross section that are…
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 $(\rho_{in},u_{in})$…
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…