Aspect on vortex lines in Euler flow.

A class of Euler flows of an ideal incompressible liquid is considered. Helical flow structures are classified by Hopf index, Brouwer degree, and linking number in geometry. A mechanism of generation and annihilation of vortex line is given. The evolution equation of the vortex line has been given and its bifurcation behavior at the critical points is also discussed in detail. Three kinds of length scales are given: l proportional to (t- t*)1/2, l proportional to t- t*, and l=const.