# Stochastic Dynamics:

## Modelling the Effects of Turbulence on Flexible
Structures

## Overview

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.

## Results

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)