  One-point time-series measurements limit the observation of three-dimensional
fully developed turbulence to one dimension. For one-dimensional models, like
multiplicative branching processes, this implies that the energy flux from
large to small scales is not conserved locally. This then renders the random
weights used in the cascade curdling to be different from the multipliers
obtained from a backward averaging procedure. The resulting multiplier
distributions become solutions of a fix-point problem. With a further
restoration of homogeneity, all observed correlations between multipliers in
the energy dissipation field can be understood in terms of simple
scale-invariant multiplicative branching processes.
