  Geometrical random multiplicative cascade processes are often used to model
positive-valued multifractal fields such as the energy dissipation in fully
developed turbulence. We propose a dynamical generalization describing the
energy dissipation in terms of a continuous and homogeneous stochastic field in
one space and one time dimension. In the model, correlations originate in the
overlap of the respective spacetime histories of field amplitudes. The
theoretical two- and three-point correlation functions are found to be in good
agreement with their equal-time counterparts extracted from wind tunnel
turbulent shear flow data.
