On the Stability of Two Basic Parallel Flows:Analysis,Progress Report and Proposal for Further Research,

摘要

This report provides a detailed technical outline and evaluation of research on the hydrodynamic stability of plane Poiseuille flow and of pipe Poiseuille flow. Each case involves significant discrepancies between the predictions of conventional theory and the results of actual experimental observations. In particular, the conventional theory fails completely to account for the well known instability of ordinary pipe flow. This report describes a more general theory which shows promise of overcoming the above limitations. The new theory involves a number of innovations in the formulation of some of the basic equations, in the formulation of certain boundary conditions, and in the formulation of the criterion of stability itself. The analytical work is essentially complete and preliminary calculations, while still of limited scope, appear to support the theory and are therefore quite encouraging.