Nonlinear Evolution of Helical Vortex Disturbed by Long-Wave Instability

The nonlinear evolution of a helical vortex disturbed by a long-wave instability mode is studied by direct numerical simulation. The 3D Navier-Stokes equations for an incompressible flow are solved using highly accurate numerical techniques assuming that the helical vortex extends periodically. Two values of the pitch are considered: L/R=0.2 and 0.3. The wavenumber of the long-wave instability mode is set to k=1/2 and 3/2. The evolution and the topology of the resulting vortices depend crucially on the pitch L/R at the nonlinear stage. In both cases, the helical vortex deforms significantly so that vortex reconnection occurs. When L/R=0.3, a vortex ring is detached from the helical vortex after the vortex reconnection. As a result, the pitch of the helical vortex is doubled. A vortex ring is also created after the vortex reconnection when L/R=0.2; however, it is linked with the remaining helical vortex after the reconnection. This linkage makes the vortex tubes interact strongly, which leads to turbulent transition.