This research is aimed at understanding universal features of turbulent flow at very high Reynolds numbers, and in particular small-scale intermittency. This is done using cascade models, which are simplified representations of the cascade of eddies observed in turbulent flow. Each octave is written as a superposition of a constant number of modes.
Eggers and Grossmann (1991) derive a cascade model by projecting the Navier-Stokes equation onto a self-similar collection of Fourier modes. Further simplification leads to a stochastic model which is analytically solvable (Eggers (1994)) , and thus allows for a detailed understanding of the dynamical mechanisms involved in the build-up of intermittent fluctuations. A detailed description and comparison of both types of models is found in (Uhlig and Eggers (1997a)) and (Uhlig and Eggers (1997b)). The multifractal model derived by Eggers and Wang (1998) describes the transition region between inertial and dissipative ranges.