The incompressible laminar axisymmetric wake

by Stanley A. Berger


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Consideration of the asymptotic development of the axisymmetric incompressible wake far behind a long, thin cylinder. Asymptotic expansion in inverse powers of the axial distance downstream breaks down when the coefficient of the inverse second power of the axial distance fails to approach zero exponentially at the edge of the wake. The axisymmetric problem is then reformulated, and solution breakdown is shown to be caused by the existence of a logarithmic term in the second-order approximation. The logarithmic term is calculated explicitly, but the next term is again indeterminate owing to neglect of the initial velocity profile at the base of the cylinder. Indeterminate factors associated with the existence of eigensolutions also appear in higher-order terms. Despite this indeterminacy, and the specific concern with the wake behind a very slender cylinder, the solution obtained has some relevance to the wake behind any axisymmetric body and should be of interest to those concerned with wake behind any axisymmetric body and should be of interest to those concerned with wake flow porblems.

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