Abstract

It is a classical problem in fluid dynamics about the stability and instability of hydrodynamic patterns in various physical settings, in particular the inviscid limit of laminar flow and boundary layer. The study can be traced back to the early work by Lord Rayleigh and Heisenberg among many others. On the other hand, one of the powerful analytic tools initiated by Sommerfeld and Orr is the spectral analysis by studying the Fourier normal mode behavior through the famous Orr-Sommerfeld equation derived from the linearization of the incompressible Navier-Stokes equations. In this talk, we will present some recent study on the Orr-Sommerfeld system derived from the linearization of the MHD system around a shear flow profile in different physical regimes and then investigate some different or similar stability and instability phenomena compared with the Navier-Stokes equations. The study also reveals the effect of the magnetic field on stability in different situations.