The stability of steady, helical vortex filaments in a tube

The nonlinear conditions for the development of helical vortex filaments in a circular tube an considered. The helical flow is assumed to be irrotatio nal, except in a vortex filament of infinitesimal core area. By introducing an appropriate image for this helical vortex filament, the boundary condit ion on the material frontier is satisfied. By assuming an axisymmetric flow upstream and imposing the conservation laws, a dependence between the heli x pitch and the nonlinear amplitude of the helical vortex developed downstr eam is obtained. Our results show that only helical flows with the pitch in a certain range of values are allowed. The dependence of this range on the swirl ratio and on the tube cross section is considered. We discuss the us efulness of the nonlinear analysis of the allowed flows to explain experime ntal results and to complement the usual linear study of stability. (C) 199 9 American Institute of Physics. [S1070-6631(99)01904-2].