Fractal Modeling of Turbulence

For now this is just a place holder to discuss topics about fractals. For related topics see my post on Kolmogorov’s Turbulance. I would like to present the quote though to illustrate the difficulty of using numerical methods to solve Naiver Stokes equations:

1.1. Statement of the problem Many flows of interest in science and engineering display complex spatial and temporal structures (eddies) spanning a wide range of scales. The ratio between the largest (L) and smallest ( )  scale can easily exceed in typical engineering applications, and can be as high as or higher in geophysical applications. Since the nonlinear interaction between eddies of different sizes eludes even the most sophisticated analytical approaches, one must resort to either extensive experimentation or direct numerical simulation (DNS) of the governing equations. The latter approach has gained strength by the rapid increase in the power of digital computers during the past 20 years. Despite this fact, DNS of flows for which the ratio $latex  L/ \eta $ is much larger than are still prohibitive

http://www.me.jhu.edu/meneveau/pdf-papers/ScottiMeneveau99.pdf

More papers on fractals and turbulance can be found here:

http://www.me.jhu.edu/~meneveau/pubs-fractals.html