On the Nonlinear Stability of Laminar Flow Between Parallel Planes

摘要

The nonlinear stability of laminar flow between parallel planes for rigid boundary condition has been studied using Lyapunov's second method.By defining an energy functional it is proved that the laminar basic flow,which includes plane Couette flow and plane Poiseuille flow as special cases,is nonlinearly unconditionally and asymptotically stable for all Reynolds numbers if the perturbations are two-dimensional and depend only on y,z and t.