The three-dimensional linearized vorticity transport equations for plane and pipe Poiseuille flow were studied using a highly generalized complex exponential form of solution in both space and time. The stability of these flows was examined using frames of reference which move with the fluid particles. Numerical results for plane Poiseuille flow show that the critical Reynolds number is lowered by the introduction of streamwise spatial decay. This result provides a new basis for improving the agreement between theory and experiment. Numerical results for pipe flow were not obtained due to a probable error in some detail of the analysis or numerical method.

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http://archive.org/details/onstabilityofpoi1094520974

Lieutenant, United States Navy