  We study a generalization of the original tree-indexed dyadic model by Katz
and Pavlovi\'c for the turbulent energy cascade of three-dimensional Euler
equation. We allow the coefficients to vary with some restrictions, thus giving
the model a realistic spatial intermittency. By introducing a forcing term on
the first component, the fixed point of the dynamics is well defined and some
explicit computations allow to prove the rich multifractal structure of the
solution. In particular the exponent of the structure function is concave in
accordance with other theoretical and experimental models. Moreover anomalous
energy dissipation happens in a fractal set of dimension strictly less than 3.
