  A class of dynamical models of turbulence living on a one-dimensional
dyadic-tree structure is introduced and studied. The models are obtained as a
natural generalization of the popular GOY shell model of turbulence. These
models are found to be chaotic and intermittent. They represent the first
example of (1+1)-dimensional dynamical systems possessing non trivial
multifractal properties. The dyadic structure allows to study spatial and
temporal fluctuations. Energy dissipation statistics and its scaling properties
are studied. Refined Kolmogorov Hypothesis is found to hold.
