Stability of Spatially Periodic Supercritical Flows in Hydrodynamics

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