The Decay of Three-dimensional Deviations from the Fully Developed State in Laminar Pipe Flow
The basic equations for the flows in circular pipes at high Reynolds numbers are derived. At a certain cross-section a three-dimensional velocity field is given which is only slightly different from the fully developed state. The decay of the deviations is investigated by linearising the basic equations leading to an eigenvalue problem. Eigenvalues and eigenfunctions are given. The decaying flow consists of various flow structures such as ring vortices as well as single, double and multiple streamwise vortices. Each of these flow structures have different decay behaviour. The swirl (single streamwise vortex) has the lowest decay. The decaying is described by means of characteristic parameters, which correspond with the various flow structures.
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