A New Look at Self-Similarity in Strained Plane Wakes

In early experiments, A. J. Reynolds and J. F. Keffer sought to determine whether plane wakes of circular cylinders, when strained by a wind tunnel of varying cross-section, evolved in accordance with an analytically derived self-similar solution. As pointed out by Reynolds, for the strain geometry considered this self-similar solution indicated exponential growth of the viscous term in the mean momentum equation, a result which he interpreted as suggesting that such wakes would eventually relaminarize. The experimental results were found not to agree with the similarity theory and recent direct numerical simulations confirm this. However, a more general self-similar analysis of the kind suggested by W. K. George is found to lead to families of possible similarity solutions, some of which do indeed describe the observed flaw behavior. These equilibrium similarity solutions result from creating a balance in the governing equations by grouping certain terms. For these solutions the viscous terms can be retained in the analysis.