PROPOSAL NO.: CTS-0442845 PRINCIPAL INVESTIGATORS: MARK STREMLER INSTITUTION: VANDERBILT UNIVERSITY
INVISCID MODELS OF TWO-DIMENSIONAL VORTEX WAKES WITH CONTINUOUS VORTICITY
Development of novel analysis methodology of periodic vortex wakes is supported under this grant. While this entails a mathematical exercise in finding solutions to the non-linear governing equation, the interest is primarily in the physical understanding of vortex wakes that can be gained from such a solution. Such vortex wakes are relevant to a number of engineering applications. While there is evidence supporting the existence of such a solution for the staggered vortex street, there is a strong possibility that it does not exist or that it cannot be expressed in closed form as proposed. This work can be considered the application of a new approach to an established research topic on two fronts. First, inviscid analysis of the staggered vortex street has focused on either point vortices or constant vorticity patches. The proposed work appears to be the first attempt to model the vortex street with a continuous vorticity field. Secondly, the analogy between solitons and vortex dynamics has led recently to several new exact solutions of the Euler equations but the approach that was used is applicable only for stationary vortex configurations. The proposed work will examine the extension of this approach to relative vortex equilibria that translate uniformly. The intellectual merit of this work will be its contributions to the fundamental understanding of basic fluid mechanics. The staggered vortex street is a classical problem in fluid mechanics and a commonly occurring physical phenomenon, and the determination of an exact solution will significantly advance the ability to investigate its intriguing behavior. In particular, the proposed work will investigate the reason for the apparent stability of the staggered street, which is still an open question. This work will also provide a framework for finding other exact solutions to the Euler equations. One anticipated outgrowth of the proposed work is a collaborative investigation of exotic vortex wakes that contain three or more vortices per period. The broader impacts of this work will include advancing discovery and understanding while promoting teaching and learning, broadening the participation of underrepresented groups, and broad dissemination of results for the enhancement of scientific and technical understanding.
