# Earth Cubed

## 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 ( $\eta$)  scale can easily exceed $10^4$ in typical engineering applications, and can be as high as $10^6$ 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 $10^2$ are still prohibitive

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

More papers on fractals and turbulance can be found here:

August 27, 2009 - Posted by | Fractals, Turbulence

1. Found this paper on another forum:
http://www.fractalforums.com/fluid-dynamics-turbulence-and-weather-prediction/which-direction/
It looks like a nice light read. 🙂

Using a Fractal Program to Model Vortical Flows
L. Kerry Mitchell, Mathematics Department, University of Advancing Technology,

Abstract
While extraordinarily complex in their physics, vortices have always been a part of human culture. This work presents a technique for simulating vortical flows using a fractal program on a personal computer. The resulting flows model real flows in some respects and demonstrate periodicity, chaos, and fractal structures. Also, the aesthetic interest of vortical flows introduces an opportunity for the artist to go beyond the spirals typically found in fractal art.

https://www.fractalus.com/kerry/articles/vortical_flow1.pdf

Comment by s243a | September 3, 2009 | Reply

2. Here are some posts about fractals at Climate Audit:

Comment by s243a | September 3, 2009 | Reply

3. A more detailed Breakdown of the link given in my above post:

Contains a simplified explanation of the delta v turbulence equations:
http://www.me.jhu.edu/meneveau/current.html

A Breakdown of turbulence topics by Categories:
http://www.me.jhu.edu/meneveau/publications.html

Comment by s243a | September 3, 2009 | Reply