Stochastic Dynamics:

Modelling the Effects of Turbulence on Flexible Structures


Many motions encountered in Nature are caused by atmospheric turbulence. Everyday example of such motions include the swirling behaviour of rising smoke and the swaying of tree-branches in the wind. Recently I have worked on the problem of simulating the latter. Since this phenomenon is difficult to key frame directly, researchers usually resort to physics-based methods. In these methods, the motion of the branches is computed by integrating the relevant dynamical equations over time. Since the forces driving these equations result from turbulent wind fields, we observe that the corresponding motions of the trees are random in nature. This observation forms the basis of my method, that of modelling the movement of the tree as a stochastic process. This process is synthesized directly by filtering an uncorrelated noise in the frequency domain. A filter is constructed by computing a small number of deformations characterizing the tree. This is done using a technique known as modal analysis in engineering. The same methodology can also be applied to other flexible structures. Indeed I was able to generate animations of flexible plates moving in a turbulent wind field, e.g., flag-like behaviours.

The technical details can be found in an INRIA technical report RR-2847 .

I am planning to apply this method to more interesting trees and structures in the near future. If you have any cool tree models and you want to see them sway in the wind drop me a line.


To give you an idea of the results one can get with this method check out the following two animations.

Simple Tree (mpeg, 340111 bytes)

Underwater Scene (mpeg, 451771 bytes)