We use momentum transfer arguments to predict the friction factor $f$ in two-dimensional turbulent soap-film flows with rough boundaries (an analogue of three-dimensional pipe flow) as a function of Reynolds number Re and roughness $r$, considering s
eparately the inverse energy cascade and the forward enstrophy cascade. At intermediate Re, we predict a Blasius-like friction factor scaling of $fproptotextrm{Re}^{-1/2}$ in flows dominated by the enstrophy cascade, distinct from the energy cascade scaling of $textrm{Re}^{-1/4}$. For large Re, $f sim r$ in the enstrophy-dominated case. We use conformal map techniques to perform direct numerical simulations that are in satisfactory agreement with theory, and exhibit data collapse scaling of roughness-induced criticality, previously shown to arise in the 3D pipe data of Nikuradse.
We simulate an individual-based model that represents both the phenotype and genome of digital organisms with predator-prey interactions. We show how open-ended growth of complexity arises from the invariance of genetic evolution operators with respe
ct to changes in the complexity, and that the dynamics which emerges is controlled by a non-equilibrium critical point. The mechanism is analogous to the development of the cascade in fluid turbulence.
