Images of Spatio-Temporal Chaos


Further above onset rolls tend to terminate with their axes orthogonal to the walls and thus become curved. They form so-called wall foci near the walls and various defects in the interior of the pattern. The foci tend to emit new rolls which compress the rolls in the sample center and cause them to become unstable. Thus a disorderd state with a very slow irregular time dependence is created.

From Y.-C. Hu, R. Ecke, and G. Ahlers, Phys. Rev. E 51, 3263 (1995).





Even further above onset a new state, known as spiral-defect chaos, is entered. It has an intrinsic irregular time dependence which is independent of the presence of any sidewalls. The image shown here was obtained from convection in carbon dioxide under pressure. During the last few years spiral-defect chaos has become a widely-studied example of spatio-temporal chaos. An mpg movie (2.3 MB) showing its dynamics can be found here (512 frames, 1 s / frame, sulfur hexafluoride, P = 20 bar, T = 38.0 deg. C, Pr = 0.87, epsilon = 0.91).

From J. Liu, K.M.S. Bajaj, and G. A., unpublished. Movie from N. Becker and G.A., unpublished.





Spiral-defect chaos is found over a wide parameter range. Here is an example obtained from convection in acetone.

From K.M.S. Bajaj, D.S. Cannell, and G. Ahlers, Phys. Rev. E 55, R4869 (1997).





Surprisingly, the roll structure in convection can become seemingly simpler again at even larger temperature differences. Above the spiral-defect chaos range the rolls organize themselves again with curvature and wall foci, and look similar to the patterns below the spiral-defect chaos onset. Here, however, we also find traveling waves moving along the roll axes.

From J. Liu, K.M.S. Bajaj, and G. Ahlers, to be published.

Spiral-defect chaos occurs well above the onset of convection. Spatio-temporal chaos is easier to understand if it evolves continuously directly out of the conduction state. This occurs in pure-fluid convection when the sample is rotated about a vertical axis for a certain range of rotation frequencies. This chaotic state is known as Kueppers-Lortz chaos, or because of its appearance also as domain chaos. An mpg movie (4.6 MB) showing its dynamics can be found here (1024 frames, 0.125 s / frame, sulfur hexafluoride, P = 20 bar, T = 38.0 deg. C, Pr = 0.87, epsilon = 0.14). In this movie the dark stripes are hot upflowing gas and the colored stripes are cold downflowing gas. The false color represents the orientation of the stripes.

From Y. Hu, W. Pesch, G. Ahlers, and R.E. Ecke, Phys. Rev. E 58, 5821(1998). Movie from N. Becker and G.A., unpublished.





Another example of chaos at onset occurs in electro-convection. Here a voltage is applied to a thin layer of a nematic liquid crystal. The pattern consists of the superposition of two sets of rolls with different angular orientations. The rolls travel in the directions perpendicular to their axes.

From M. Dennin, G. Ahlers, and D.S. Cannell, Science 272, 388 (1996).





Using Fourier analysis, it is possible to determine the envelope of each set of rolls in the previous picture separately. This envelope varies irregularly (chaotically) in space. It is also chaotically time dependent.

From M. Dennin, G. Ahlers, and D.S. Cannell, Science 272, 388 (1996).





Here is the envelope of the other set of rolls.

From M. Dennin, G. Ahlers, and D.S. Cannell, Science 272, 388 (1996).





There are many other examples of chaotic spatio-temporal structures. Here is one which occurs in pure-fluid Rayleigh-Benard convection with rotation. An mpg movie (1 MB) showing its dynamics can be found here.

From K.M.S. Bajaj and G. Ahlers, unpublished.


Home - About us - News - Members - Alumni - Pattern Formation - Critical Phenomena - Recent Publications - Collaborators
Quantum Institute - Physics Department - UC Santa Barbara