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Flow generated by a small oscillating cylinder in a mixing layer
Published online by Cambridge University Press: 26 April 2006
Abstract
We study the flow generated by a small circular cylinder in a mixing layer. The cylinder is executing an oscillatory translation whose frequency is within the range of unstable frequencies of the shear layer. The smallness of the cylinder is measured by the ratio of its radius to the characteristic thickness of the layer. This (small) ratio serves as the expansion parameter for our theory; the flow naturally divides into inner and outer regions. The former is in the immediate vicinity of the cylinder and the latter is the far field which contains the instability waves. The solution to this problem is obtained by the method of matched asymptotic expansion. One objective is to study the dependence of this solution on various parameters such as the frequency of oscillation, velocity ratio, etc., and thus shed light on the associated receptivity. Other objectives deal with a restatement of causality and with the hydrodynamic field near the streamwise location of the cylinder. We find that receptivity is a strong function of frequency and velocity ratio and that the local hydrodynamic field may be quite large. Causality is restated in terms of the well-known exponential integral.
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