Related papers: Unstable mode around the 3D boundary layer flow
In this paper, we construct growing modes of the linearized Navier-Stokes equations about generic stationary shear flows of the boundary layer type in a regime of sufficiently large Reynolds number: $R \to \infty$. Notably, the shear…
Computer simulations of sheared granular fluids, modeled as inelastic hard spheres, are presented which show signs of a uniquely three-dimensional instabilty. In the stable regime, a linear velocity profile, $v_{x}=ay$, with shear rate $a$…
In this paper we study the nonlinear stability of a shear layer profile for Navier Stokes equations near a boundary. This question plays a major role in the study of the inviscid limit of Navier Stokes equations in a bounded domain as the…
In this paper, we investigate the incompressible steady Navier-Stokes system with Navier slip boundary condition in a two-dimensional channel. As long as the width of cross-section of the channel grows more slowly than the linear growth,…
It is a classical problem in fluid dynamics about the stability and instability of different hydrodynamic patterns in various physical settings, in particular in the high Reynolds number limit of laminar flow with boundary layer. However,…
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…
In this paper, we develop a stability threshold theorem for the 2D incompressible Navier-Stokes equations on the channel, supplemented with the no-slip boundary condition. The initial datum is close to the Couette flow in the following…
Wall-bounded turbulent shear flows are known to exhibit universal small-scale dynamics that are modulated by large-scale flow structures. Strong pressure gradients complicate this characterization, however; they can cause significant…
We study the $L^{\infty}$ stability of the 2D Navier-Stokes equations with a viscosity-dependent Navier boundary condition around shear profiles which are linearly unstable for the Euler equation. The dependence from the viscosity is given…
This paper concerns spectral instability of shear flows in the incompressible Navier-Stokes equations with sufficiently large Reynolds number: $R\to \infty$. It is well-documented in the physical literature, going back to Heisenberg, C.C.…
In this paper, we investigate the instability of the trivial steady states to the incompressible viscous fluid with Navier-slip boundary conditions. For the linear instability, the existence of infinitely many normal mode solutions to the…
In this paper, we obtain the optimal instability threshold of the Couette flow for Navier-Stokes equations with small viscosity $\nu>0$, when the perturbations are in the critical spaces $H^1_xL_y^2$. More precisely, we introduce a new…
The stability of a three-dimensional, incompressible, viscous flow through a finite-length duct is studied. A divergence-free basis technique is used to formulate the weak form of the problem. A SUPG (streamingline upwind Petrov-Galerkin)…
Despite the physical importance, there are limited mathematical theories for the compressible Navier-Stokes equations with strong boundary layers. This is mainly due to the absence of a stream function structure, unlike the extensively…
We advance the computation of physical modal expansions for unsteady incompressible flows. Point of departure is a linearization of the Navier-Stokes equations around its fixed point in a frequency domain formulation. While the most…
We investigate the global in time stability of regular solutions with large velocity vectors to the evolutionary Navier-Stokes equation in ${\bf R}^3$. The class of stable flows contains all two dimensional weak solutions. The only…
This paper concerns the instability and stability of the trivial steady states of the incompressible Navier-Stokes equations with Navier-slip boundary conditions in a slab domain in dimension two. The main results show that the stability…
The flow of the laminar boundary layer on a flat plate is studied with simulation of Navier-Stokes equations. The mechanisms of flow instability at external edge of the boundary layer and near the wall are analyzed using the energy gradient…
The existence and dynamical role of particular unstable Navier-Stokes solutions (exact coherent structures) is revealed in laboratory studies of weak turbulence in a thin, electromagnetically-driven fluid layer. We find that the dynamics…
This paper is devoted to the study of the nonlinear instability of shear layers and of Prandtl's boundary layers, for the incompressible Navier Stokes equations. We prove that generic shear layers are nonlinearly unstable provided the…