Threshold Amplitudes for Transition in Channel Flows

The threshold amplitude for subcritical transition in Poiseuille and Couette flows is investigated. For Poiseuille flow we present examples where the threshold scales like ß R \Gamma7=4 for 1500 R 5000, where R is the Reynolds number. For Couette flow we present an example where the threshold scales like ß R \Gamma5=4 for 500 R 2000. 1. Introduction It has been demonstrated that turbulence can appear in plane Poiseuille and Couette flows at Reynolds numbers R as low as ß 1000 (Patel and Head, 1969; Carlson, Widnall and Peeters, 1982) and ß 360 (Lundbladh and Johansson, 1991; Tillmark and Alfredsson 1992), respectively. Here R is based on the channel half-height and the difference between the wall and centerline velocities. On the other hand, linear analysis predicts that Poiseuille flow can be unstable only if R ? R c ß 5772 (Orszag, 1971) and that Couette flow is stable for all Reynolds numbers (Romanov, 1973). At supercritical Reynolds numbers an infinitesimally small dis..