Quasi-equilibrium states for helical vortices with swirl

We present a family of exact equilibrium solutions the Euler equations consisting single helical vortex with an axial flow component along core. Relations between vorticity, velocity and streamfunction are analytically derived in inviscid framework constitute generalization relations valid for rings (Batchelor, 1967 An Introduction to Fluid Dynamics . Cambridge University Press). Through Navier–Stokes simulations, it is shown that these hold quasi-steady viscous become independent Reynolds number when sufficiently large. also elaborate procedure which generates quasi-equilibrium prescribed characteristics (circulation, helix radius, pitch, core size, swirl level) compare obtained state results asymptotic theory. Finally, we illustrate how strong jeopardizes such evolution towards quasi-equilibrium.