  We consider transition to strong turbulence in an infinite fluid stirred by a
gaussian random force. The transition is {\bf defined} as a first appearance of
anomalous scaling of normalized moments of velocity derivatives (dissipation
rates) emerging from the low-Reynolds-number Gaussian background. It is shown
that due to multi-scaling, strongly intermittent rare events can be
quantitatively described in terms of an infinite number of different "Reynolds
numbers" reflecting multitude of anomalous scaling exponents. The theoretically
predicted transition disappears at $R_{\lambda}\leq 3$. The developed theory,
is in a quantitative agreement with the outcome of large-scale numerical
simulations.
