Images of Convection Patterns near Onset

Even below the point of instability of the spatially-uniform conduction-state there are fluctuating patches of convection rolls which are driven by thermal noise (left image), but they are only barely resolved with modern flow visualization techniques. However, their Fourier analysis yields a spatial power spectrum (right image) which clearly reveals a characteristic wavenumber (radius of the ring) and which shows that the Rayleigh-Benard system is isotropic in the plane (i.e. there is no preferred direction but rather a uniform ring in Fourier space).

From M. Wu, G. Ahlers, and D.S. Cannell, Phys. Rev. Lett. 75, 1743 (1995).

The natural planform of Rayleigh-Benard convection just above onset consists of straight rolls. This pattern was obtained in a cell with uniform spacing in the center section which is shown. At larger radii, there was a radial ramp of the spacing which gradually reduced the convection amplitude to zero.

From K.M.S. Bajaj, N. Mukolobwiez, N. Currier, and G. Ahlers, Phys. Rev. Lett. 83, 5282 (1999).

When the cell has the usual rigid sidewall, the straight-roll pattern in the interior develops defects near the wall because the rolls tend to terminate with their axes perpendicular to the wall.

From Y.Hu, R. Ecke, and G. Ahlers, Phys. Rev. E 48, 4399 (1993).

When the properties of the fluid vary significantly over the imposed temperature difference, hexagons occur near the onset of convection. Note the perfect, defect-free hexagonal order of this very large pattern! This example was obtained with carbon dioxide under pressure as the fluid.

From E. Bodenschatz, J.R. de Bruyn, G. Ahlers, and D.S. Cannell, Phys. Rev. Lett. 67, 3078 (1991).

If you would like to see hexagons in more detail, please go to Hexagons near Onset

Hexagons can occur also in convection of more unusual fluids. Here is an example where the nematic liquid crystal 5CB was used.

From L. Thomas, W. Pesch, and G. Ahlers, Phys. Rev. E, 58, 5884 (1998).

The flow in the center of the cells making up a hexagonal lattice can be up or down, depending on the particular properties of the fluid. Here is an example from two-phase convection, where the interface between the phases can be either near the top or near the bottom of the sample.

From G. Ahlers, in Pattern Formation in Liquid Crystals, edited by L. Kramer and A. Buka (Springer, 1996).

Concentric rolls, and giant spirals with one or more arms, can also be stabilized near the convective onset when the lateral boundaries provide a small horizontal temperature gradient near them. Each spiral arm terminates at the outer end in a defect. The spirals rotate slowly.

From E. Bodenschatz, J.R. de Bruyn, G. Ahlers, and D.S. Cannell, Phys. Rev. Lett. 67, 3078 (1991).

Rolls and hexagons are not the only patterns found at the onset of convection. This pattern of squares was obtained using a mixture of ethanol and water as the fluid.

From M.A. Dominguez-Lerma, G. Ahlers, and D.S. Cannell, Phys. Rev. E. 52, 6159 (1995).

It was a surprise to find that squares also occur near onset in pure-fluid convection when the apparatus is rotated around a vertical axis. This example was obtained using Argon under pressure.

From K.M.S. Bajaj, J. Liu, B. Naberhuis, and G. Ahlers, Phys. Rev. Lett. 81, 806 (1998).

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