9404086 Childress This research will be concerned with structure of the vorticity and magnetic fields in complex flows, in the limit of vanishing dissipation. The work is an outgrowth of kinematic studies of fast dynamos, or dynamos which operate in the limit of infinite magnetic Reynolds number. We propose further work on this problem, involving models and asymptotic techniques developed in the previous studies, which link the dynamo action to a combination of stretching and folding of field lines. We shall also extend the scope of our work to include dynamical self-consistency of motions producing a fast dynamo. In an new direction, we shall apply the Lagrangian techniques of kinematic fast dynamo theory to the structure of vorticity in fully-developed turbulence. The new feature here is the use of pulsed Lagrangian maps of the vorticity field which conserved energy locally. We shall study a class of ``eddy structure'' models to understand how the Kolmogorov cascade responds to various boundary conditions and driving mechanisms. These models may provide a useful tool for pin-pointing the form of eddy structure in the inertial range. The primary motivation of this work is an understanding of astrophysical turbulence and the associated magnetic fields of the cosmos. Dissipation, such as is introduced in ordinary fluids by viscosity, for example, is essentially absent in these enormous systems. The convection zone of the Sun is a nearby system of this kind, where turbulence and magnetic fields commingle. Our aim is to understand the connection between the fluid flow, the turbulence itself, and certain fields, magnetic and vortical, embedded in it. These two fields are quite different in their dynamics, but they share certain geometrical features which emerge in the analysis of models. We intend to exploit these connections and bring to bear mathematical tools developed for the simpler magnetic problem, in the hope of understanding uncovering important f eatures of the physical structure of vorticity in fully developed turbulence. ***
