# Condensed Matter seminar: "Roughness-induced criticality and the statistical mechanics of turbulence in pipes and soap films"

Are fluid turbulence and critical phenomena analogous to one another? In this talk, I explain that this connection may be deeper than has been previously thought. Indeed, I argue that one can use these insights to understand turbulence, in an attempt to emulate the pattern of discovery which led to the solution of the phase transition problem. I show that these ideas lead to the prediction of a novel scaling law --- a manifestation of what I term roughness-induced criticality --- that has been verified by analyzing experimental data on turbulent pipe flows, taken by Nikuradze in 1933. I review how the friction experienced by turbulent fluids can be captured quantitatively as a function of flow velocity and wall-roughness, by momentum-transfer arguments due to Gioia and Chakraborty, and describe how this theory and the roughness-induced criticality theory are currently being tested by direct numerical simulations and experiments on two-dimensional turbulent flows in soap films.

References:

- Nigel Goldenfeld. Roughness-induced criticality in a turbulent flow.
*Phys. Rev. Lett.***96**, 044503:1-4 (2006). - N. Guttenberg and Nigel Goldenfeld. The friction factor of two-dimensional rough-boundary turbulent soap film flows arXiv:0808.1451v4 (2008)
- G. Gioia and P. Chakraborty. Turbulent friction in rough pipes and the energy spectrum of the phenomenological theory.
*Phys. Rev. Lett.*96, 044502:1-4 (2006).