The hydromagnetic stability of stratified shear flows in the presence of cross flows is discussed. The magnetic field is applied in the direction of the main flow. Some necessary conditions of instability, the growth rate of unstable modes and reduction of the unstable region are discussed.
In an earlier paper [5] a method for eigenvalue inclussion using a Gerschgorin type theory originating from Donnelly [2] was applied to the plane Orr-Sommerfeld problem in the case of a pure Poiseuile flow. In this paper the same method will be used to deal Poiseuile and Couette flow. Potter [6] has treated this case before with an approximative method.
We consider a 2D mathematical model describing the motion of a solution of surfactants submitted to a high shear stress in a CouetteTaylor system. We are interested in a stabilization process obtained thanks to the shear. We prove that, if the shear stress is large enough, there exists global in time solution for small initial data and that the solution of the linearized system (controlled by a nonconstant parameter) tends to 0 as goes to infinity. This explains rigorously some experiments.
We consider a 2D mathematical model describing the motion of a solution of surfactants submitted to a high shear stress in a Couette-Taylor system. We are interested in a stabilization process obtained thanks to the shear. We prove that, if the shear stress is large enough, there exists global in time solution for small initial data and that the solution of the linearized system (controlled by a nonconstant parameter) tends to 0 as t goes to infinity. This explains rigorously some experiments. ...
Two-dimensional inviscid channel flow of an incompressible fluid is considered. It is shown that if the flow is steady and features no horizontal stagnation, then the flow must necessarily be a parallel shear flow.
In this paper we study the derivation of homogeneous hydrostatic equations starting from 2D Euler equations, following for instance [2,9]. We give a convergence result for convex profiles and a divergence result for a particular inflexion profile.