V. Shtern et al., GENERATION OF SWIRL DUE TO SYMMETRY-BREAKING, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 49(4), 1994, pp. 2881-2886
We study symmetry breaking in a meridional steady motion of viscous in
compressible fluids by considering the case of a laminar axisymmetric
''vortex dynamo.'' Using a linear and subsequently a non-linear analys
is we demonstrate the feasibility of a supercritical pitchfork birfurc
ation from an initially ''trivial'' nonswirling flow solution to one w
ith a steady (clockwise or counterclockwise) swirling regime as the Re
ynolds number exceeds a critical value. This agrees with recent experi
mental results for a flow inside a conical meniscus, as observed in el
ectrosprays.