Nonlinear cellular motions in Poiseuille channel flow

摘要: We expand the equations describing plane Poiseuille flow in Fourier series co-ordinates parallel to bounding walls. There results an infinite system of for amplitudes, which are functions time and cross-stream co-ordinate. This is drastically truncated resulting set solved accurately by a finite difference method. Three truncations considered: (I) single mode with dependence only on downstream co-ordinate time, (II) plus its first harmonic, (III) three-dimensional mode. For all three cases, variety initial conditions, solutions evolve steady state as seen particular moving frame reference. No runaways encountered.