- Dowell, E.H., Non-linear theory of unstable plane Poiseuille flow,
J. Fluid Mech. (UK), vol. 38
pp. 401 - 14 .
(last updated on 2007/04/10)
A theoretical study of plane Poiseuille flow is made using the full non-linear Navier-Stokes equations. The mathematical technique employed is to use a Fourier decomposition in the streamwise spatial variable, a Galerkin expansion in the lateral variable and numerical integration with respect to time. By retaining the non-linear terms, the limit cycle oscillations of an unstable (in a linear sense) flow are obtained. A brief investigation of the possibility of instability due to large (non-linear) disturbances is also made. The results are negative for the cases examined. Comparisons with results previously obtained by others from linear theory illustrate the accuracy and efficacy of the method