We analyse experimental velocity measurements on the axis of a low temperat
ure gaseous helium jet. From independent increments arguments, we reproduce
the behaviour of structure functions. We show where this approach fails an
d how the intermittency phenomenon is a small correction. The physical argu
ments under the multiplicative cascade models for this intermittency imply
an acceleration of this cascade close to the dissipative range, which we ar
e able to evidence. This acceleration could be responsible of the apparent
Extended Self Similarity between structure functions of various orders.