SCALE-INVARIANT CASCADES IN TURBULENCE AND EVOLUTION

In this dissertation, I present work addressing three systems which are traditionally considered to be unrelated: turbulence, evolution, and social organization. The com-monality between these systems is that in each case, microscopic interaction rules give rise to an emergent behavior that in some way makes contact with the macroscopic scale of the problem. The open-ended evolution of complexity in evolving systems is analogous to the scale-free structure established in turbulent \ud ows through local transportation of energy. In both cases, an invariance is required for the cascading behavior to occur, and in both cases the scale-free structure is built up from some initial scale from which the behavior is fed. In turbulence, I examine the case of two-dimensional turbulence in order to sup-port the hypothesis that the friction factor and velocity prole of turbulent pipe \ud ows depend on the turbulent energy spectrum in a way unpredicted by the classic Prandtl theory. By simulating two-dimensional flows in controlled geometries, either an in-verse energy cascade or forward enstrophy cascade can be produced. The frictio