The Resolution of the Domain Chaos Puzzle for Rotated Rayleigh-B\'enard Convection

Due to the K\"uppers-Lortz instability, Rayleigh-B\'enard convection-patterns exhibit spatio-temporal chaos at the onset of convection when the sample rotates fast enough about a vertical axis. Previous work showed that the scaling of the correlation length $\xi$ determined from the experimental chaotic patterns disagreed with the prediction from a Ginzburg-Landau weakly-nonlinear model.\footnote{Y.-C. Hu, R. Ecke, and G. Ahlers, Phys. Rev. Lett. {\bf 74}, 5040 (1995).} Commonly the power spectrum of the pattern images (the structure factor) is used to extract $\xi$ from the half-width of its peak. Past experiments and simulations used standard Fourier techniques to calculate the power spectrum. On the basis of simulations using the Swift-Hohenberg equation, we show that those results are influenced strongly by the finite image-size available from experiment. The disagreement between experiment and theory was resolved by using the maximum-entropy method to calculate the power spectra. The maximum-entropy method is not as sensitive to the finite image-size effect. When applied to new experimental images, it yielded results for $\xi$ that were in agreement with the theory.