Abstract
In this paper we have obtained different families of exact solutions for incompressible generalized Beltrami flows. We derive all possible polynomial solutions of incompressible axisymmetric generalized Beltrami flows in the variables r and z in cylindrical coordinates. We obtain Hill’s spherical vortices and Wang’s long circulating regions as special cases of these polynomial solutions. Some other particular polynomial solutions which have special vortex configurations inside a closed stream surface are also given. In addition to polynomial solutions, we have also derived four families of exact solutions to the generalized Beltrami flows, and all these solutions are new solutions. We have shown that all the polynomial solutions to the generalized Beltrami flows are particular cases of these general solutions.
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