相关论文: Bounds for the threshold amplitude for plane Couet…
Exact solutions are obtained for the steady flow of a power-law fluid between parallel plates with partial slip conditions and uniform cross flow. The problem is properly formulated and similarities are exploited. The exact solutions are…
The transition of the flow in a duct of square cross-section is studied. Like in the similar case of the pipe flow, the motion is linearly stable for all Reynolds numbers; this flow is thus a good candidate to investigate the 'bypass' path…
We consider front propagation in a reactive Boussinesq system in an infinite vertical strip. We establish nonlinear stability of planar fronts for narrow domains when the Rayleigh number is not too large. Planar fronts are shown to be…
An outline of the state space of planar Couette flow at high Reynolds numbers ($Re < 10^5$) is investigated via a variety of efficient numerical techniques. It is verified from nonlinear analysis that the lower branch of {\it Hairpin Vortex…
We consider the compressible Navier--Stokes equation in a perturbed half-space with an outflow boundary condition as well as the supersonic condition. For a half-space, it has been known that a certain planar stationary solution exist and…
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…
In this paper, we investigate nonlinear stability of planar steady Euler flows related to least energy solutions of the Lane-Emden equation in a smooth bounded domain. We prove the orbital stability of these flows in terms of both the $L^s$…
In their way to/from turbulence, plane wall-bounded flows display an interesting transitional regime where laminar and turbulent oblique bands alternate, the origin of which is still mysterious. In line with Barkley's recent work about the…
We consider a 2D incompressible and electrically conducting fluid in the domain $\mathbb{T}\times\mathbb{R}$. The aim is to quantify stability properties of the Couette flow $(y,0)$ with a constant homogenous magnetic field $(\beta,0)$ when…
Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous applied and control problems. Yet, practically valuable results are rare in this area. This paper develops a novel approach, which…
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…
This paper carries out a linear stability analysis of a plane Couette flow in a porous layer underlying a fluid layer where the porous layer is anisotropic and inhomogeneous. The plane Couette flow is induced due to the uniform movement of…
This paper concerns the dynamics of a layer of incompressible viscous fluid lying above a rigid plane and with an upper boundary given by a free surface. The fluid is subject to a constant external force with a horizontal component, which…
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…
The linear marginal instability of an MHD Taylor-Couette flow of infinite vertical extension is considered. For hydrodynamically unstable flows the minimum Reynolds number exists even without a magnetic field, but there are also solutions…
In this paper we prove the asymptotic stability of the Kolmogorov flow on a non-square torus for perturbations $\omega_0$ satisfying $\|\omega_0\|_{H^3}\ll\nu^{1/3}$, where $0<\nu\ll1$ is the viscosity. Kolmogorov flows are important…
We consider the stability of a system of equations which are a singular perturbation of the incompressible rigid-plastic flow equations used to model granular flow. A linear stability analysis shows that solutions of these equations are…
In this paper, we consider the Boussinesq equations with magnetohydrodynamics convection in the domain $\mathbb{T} \times \mathbb{R}$ and establishes the nonlinear stability of the Couette flow $(\mathbf{u}_{sh} = (y,0), \mathbf{b}_{sh} =…
We analyze the stability of a cylindrical Couette flow under the imposition of a weak axial flow in case of a very short cylinder with a narrow annulus gap. We consider an incompressible viscous fluid which is contained in the narrow gap…
It is shown that homogeneous Rayleigh-Benard flow, i.e., Rayleigh-Benard turbulence with periodic boundary conditions in all directions and a volume forcing of the temperature field by a mean gradient, has a family of exact, exponentially…