On spatially-growing finite disturbances in plane Poiseuille flow

Abstract

Possible solutions of the Navier-Stokes equations are given representing certain finite disturbances in plane Poiseuille flow which vary with distance parallel to the bounding walls. These solutions are based on infinitesimal disturbances which vary exponentially with distance (upstream or downstream) instead of with time, and they are more closely related to the disturbances investigated experimentally than the corresponding ‘time-dependent’ solutions.