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An approximate solution to the two-dimensional incompressible fluid equations is constructed by expanding the vorticity field in a series of derivatives of a Gaussian vortex. The expansion is used to analyze the motion of a corotating Gaussian vortex pair, and the spatial rotation frequency of the vortex pair is derived directly from the fluid vorticity equation. The resulting rotation frequency includes the effects of finite vortex core size and viscosity and reduces, in the appropriate limit, to the rotation frequency of the Kirchhoff point vortex theory. The expansion is then used in the low Mach number Lighthill equation to derive the far-field acoustic pressure generated by the Gaussian vortex pair. This pressure amplitude is compared with that of a previous fully numerical simulation in which the Reynolds number is large and the vortex core size is significant compared to the vortex separation. The present analytic result for the far-field acoustic pressure is shown to be substantially more accurate than previous theoretical predictions. The given example suggests that the vorticity expansion is a useful tool for the prediction of sound generated by a general distributed vorticity field.


Copyright 2007 Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America.

The following article appeared in Raymond J. Nagem, Guido Sandri, and David Uminsky. Vorticity dynamics and sound generation in two-dimensional fluid flow. The Journal of the Acoustical Society of America, 122(1):128–134, 2007. and may be found at