We introduce a one-dimensional model of a turbulent velocity field. It consists of a superposition of successively smaller eddies, forming a Cayley-tree-like structure. The randomness of the eddy decay is modeled by a multiplier distribution p(s), whose parameters can be determined from experiment. In contrast to other cascade models, which are not stated in terms of the velocity field, every other quantity of the turbulent flow can now be calculated consistently. Scaling relations between the statistics of the velocity and the dissipation fields are shown to depend greatly on physical assumptions about the cascade. Specifically, we study the influence of the spatial coherence of eddies, and of the action of the viscous cutoff.

• Received 27 June 1991

DOI:https://doi.org/10.1103/PhysRevA.45.2360