Analytical solutions for two hollow vortex configurations in an infinite channel

作者：Green Christopher C^*

来源：European Journal of Mechanics - B: Fluids , 2015, 54: 69-81.

DOI：10.1016/j.euromechflu.2015.06.013

• Hollow vortex
• Channel
• Free boundary problem
• Free streamline theory
• Conformal mapping
• Schottky-Klein prime function

New analytical solutions for a co-travelling hollow vortex pair and a single row of hollow vortices in an infinite channel are presented. These new solutions generalise several known classical solutions for hollow vortices. The mathematical problems to be solved in each geometry are particular types of free boundary problem over a multiply connected domain. We present concise formulae for the conformal mapping determining the shape of the boundaries of the hollow vortices in both channel geometries by employing free streamline theory in combination with the function theory of the Schottky-Klein prime function. Various properties of the solutions are also presented.

• 出版日期2015-12