Spatiotemporal Chaos

Although a great deal is now known about low dimensional chaos - the erratic motion of dynamical systems described by a few variables - much less is understood about systems where the number of chaotic degrees of freedom becomes very large. One example of such a system is a spatial array of coupled chaotic elements. Typically such sytems show disorder in both space and time and are said to exhibit spatiotemporal chaos. We might hope that a statistical description of a very large (or infinite) number of degrees of freedom could be simpler than a detailed description of an intermediate number (say 10-100) of degrees of freedom.

At the present stage of our knowledge, it is important to be guided in our theoretical attack by the experimental phenomena. We have therefore been studying, using numerical simulations of equations that model the fluid dynamics, systems that are also being investigated experimentally.

The research leading to the results presented here was supported by the NSF.

Spiral Chaos

Spiral Chaos. (Click for 200 kbyte mpeg movie or here for a longer 1.2 Mbyte movie)
These are results from numerical simulations of a model for Rayleigh-Benard Convection

Spiral choas in convection was discovered experimentally by Morris, Bodenshatz, Cannell and Ahlers. A description of some experimetal results can be found here. Although dynamic spiral states are familiar in chemical and biological systems where the underlying instability is to waves, the state was completely unexpected in Rayleigh-Benard convection where the instability is to a stationary stripe state (the convection rolls). The state is even more intriguing since straight parallel rolls are thought to be stable at the same parameter values at which the dynamic spiral state is seen.

We have attempted to explain the existence of the state in terms of what we call invasive defects. A copy of the paper is on the Los Alamos preprint library..

Domain Chaos

If a convection apparatus is rotated about a vertical axis, the Coriolis forces change the fluid motion. For large enough rotation rates the stationary stripe pattern becomes unstable to a dynamic pattern of carniverous domains i.e. patches of rolls at one orientation eat up neighboring patches at some other orientation, in turn to be eaten by a third set of patches e.t.c.

These are results from numerical simulations of a model for rotating Rayleigh-Benard Convection

Domain Chaos. (Click for 260 kbyte mpeg movie)

We can look at the same dynamics in a number of different representions.

Stripe Orientation. (Click for 340 kbyte mpeg movie)
To make the domains clearer we can simply show the orientation of the stripes at each point, here plotted using a circular rainbow color scale from 0 to 180 degrees.

Domain Walls. (Click for 160 kbyte mpeg movie)
Alternatively we cal look at the domain wall motion - extracted from the data as regions where the amplitude of the stripe pattern is supressed.

You can also see longer domain (1400 kbyte) or domain wall (650 kbyte) movies (more of the same!).

[MCC Home Page]  [Table of Contents]  [Condensed Matter Physics Home Page]

The research leading to the results presented here was supported by the NSF.

Last modified Monday, March 24, 1997
Michael Cross