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).

In a thin layer of a nematic liquid crystal there is a preferred direction because the elongated nematic molecules can be oriented in a more or less uniform way. In that case the fluctuations below onset do not produce a ring in Fourier space.

From X.-L. Qiu and G. Ahlers, Phys. Rev. Lett., in print.

An mpg movie (7 MB) showing the time evolution after a step from below onset at eps_0 = -1 to above onset at eps_1 = 0.0040 can be found here (drive freq. 25 Hz, eps_0 = -1, eps_1 = 0.0040, 1.5xreal time, tot. time = 77 sec).

An mpg movie (6.7 MB) showing the time evolution of its structure factor (square of the modulus of the Fourier transform) after such a step can be found here (drive freq. 25 Hz, eps_0 = -1, eps_1 = 0.0040, 1.5xreal time, tot. time = 77 sec).

An mpg movie (7 MB) showing its time evolution after a step from below to above onset can be found here (drive freq. 4000 Hz, eps_0 = -1, eps_1 = 0.0056, 1.5xreal time, tot. time = 77 sec).

An mpg movie (6.7 MB) showing the time evolution of its structure factor (square of the modulus of the Fourier transform) after such a step can be found here (drive freq. 4000 Hz, eps_0 = -1, eps_1 = 0.0056, 1.5xreal time, tot. time = 77 sec).