On Exact Solutions of the Navier-Stokes Equations for Uni-directional Flows

2015/03/17 by F. Lam, Lam, F.
Chemical Engineering · Engineering · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Fluid Dynamics and Vibration Analysis #Rheology and Fluid Dynamics Studies

paper · pdf · doi:10.48550/arxiv.1503.05149

openalex publication_date 2015/03/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In the present note, we show that the uni-directional flows in a rectangular channel and in a circular pipe are exact spatio-temporal solutions of the Navier-Stokes equations over a short time interval. We assert that the classical plane Poiseuille-Couette flow and Hagen-Poiseuille flow are time-independent approximations of the exact solutions if an appropriate initial velocity distribution at starting location is specified. Conceptually, there do not exist absolute steady flows starting from unspecified initial data. The classic experimental measurements by Poiseuille can be explained in terms of the evolutional solutions. In particular, the pipe flow does not have a time-independent characteristic velocity. The orthodox notion that the parabolic profile exists for arbitrary Reynolds numbers is unwarranted.

Citations

• Short-time evolution of pipe Poiseuille flow
• Integral Invariance and Non-linearity Reduction for Proliferating Vorticity Scales in Fluid Dynamics

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