A family of helically symmetric vortex equilibria

We present a family of steadily rotating equilibrium states consisting of helically symmetric vortices in an incompressible inviscid irrotational unbounded fluid. These vortices are described by contours bounding regions of uniform axial vorticity. Helical symmetry implies material conservation of axial vorticity (in the absolute frame of reference) when the flow field parallel to vortex lines is proportional to (1+^ε2r²) ^-1/2, where ε is the pitch and r is the distance from the axis. This material conservation property enables equilibria to be calculated simply by a restriction on the helical stream function. The states are parameterized by their mean radius and centroid position. In the case of a single vortex, parameter space cannot be fully filled by our numerical approach. We conjecture multiply connected contours will characterize equilibria where the algorithm fails. We also consider multiple vortices, evenly azimuthally spaced about the origin. Stability properties are investigated numerically using a helical CASL algorithm.