Earth Cubed

Distributed Climate Science and Computing

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:

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

Advertisements

August 27, 2009 - Posted by | Fractals, Turbulence

3 Comments »

  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:

    Fractals And Turbulence
    Fractal properties of ST and interpretation of ST data”

    Comment by s243a | September 3, 2009 | Reply


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: