Turbulence in the heat flow of helium II manifests itself as a tangle
of quantized vortex lines. It has been known for some time that there
are two different forms of turbulence, called the T-l and the T-2 turb
ulent states. Experiments show that when a critical velocity is exceed
ed there is a large increase of the superfluid vortex line density and
a transition occurs from T-l to T-2. Until now, the nature of the two
turbulent states and of the critical velocity has been a mystery. We
present a model which solves this problem by addressing for the first
time the issue of the stability of the normal fluid. The computed tran
sition is found to be in good agreement with the observations.