On the stability of fully developed flow in a pipe

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Abstract
The stability of infinitesimal axially symmetric disturbances in fully developed pipe flow is examined anew. The classical eigenvalue problem is treated in part by asymptotic methods and leads to an algebraic relation between the eigenvalue c, the disturbance wavelength 2π/α, and the Reynolds number. Examination of the limiting cases of this relation reveals the existence of two families of characteristic numbers, the value of which tends to unity and to zero as the Reynolds number increases without bounds. For the latter, a more accurate solution is required and given. It is found that all eigenvalues yield stable solutions and that for a given wave number and Reynolds number only a finite number of eigenvalues exists.The limitations of the analysis are discussed in the light of a recent experimental study of the same problem.