Stability of Spatially Periodic Supercritical Flows in Hydrodynamics

摘要: Recently, Eckhaus developed a theory for class of nonlinear stability problems which can be formulated in terms scalar partial differential equation with quadratic nonlinearities. It is demonstrated that Eckhaus' work on the development and periodic solutions extended to matrix equations. The equations governing axisymmetric viscous flow between concentric rotating cylinders belong considered. When Taylor number T slightly above minimum critical value Tc there exists an interval possible equilibrium flows (Taylor‐vortex flows) growing out instability Couette flow. shown within Taylor‐vortex flows, subinterval stable vortex flows.