THE STABILITY OF FLOW IN AN ELLIPTIC PIPE WITH LARGE ASPECT RATIO

摘要

The stability of Poiseuille flow in an elliptic pipe with large aspect ratio is examined by regarding the flow as a perturbation of plane Poiseuille flow. It is shown that the critical Reynolds number is increased by the perturbation and the amplitude equation for the nonlinear development of small disturbances is found. A quasisteady solution of the amplitude equation is shown to exist at subcritical Reynolds numbers, but it is unstable.