Convective pattern evolution and secondary instabilities

Abstract

Using an automated laser-Doppler scanning technique, we have performed an extensive study of pattern evolution and instabilities in a large Rayleigh-BBnard cell (20 by 30 times the layer depth) at moderate Prandtl number (2.5). This work differs from earlier experiments in that the Doppler mapping technique permits both the spatial structure and time evolution of the velocity field to be quantitatively studied, and runs lasting up to ten thousand vertical thermal diffusion times are presented. We observe and document the properties of three qualitatively different regimes above the critical Rayeigh number R c . (i) Below 5 R c , there are a number of simple patterns in which the rolls align perpendicular to all lateral cell boundaries. The patterns are therefore curved and generally contain two boundary-related defects. A change in R induces patterns with many defects, which evolve toward the simple patterns over extraordinarily long times. These features seem to be consistent with theoretical models based on the competition between boundary, curvature and defect contributions to a Liapunov functional. However, stable states are not always reached. (ii) Above 5 R c the skewed-varicose instability of Busse & Clever causes progressively faster broadband time dependence with a spectral tail falling off approximately as the fourth power of the frequency. Doppler imaging shows that the fluctuations are caused by narrowing and pinching off of the rolls. (iii) Above 9 R c both the oscillatory and skewed-varicose instabilities cause local velocity fluctuations. However, substantial mean roll structure persists even over a 40 h period (one horizontal thermal diffusion time) at 1 5 R c . Velocity power spectra with two distinct maxima associated with the two instabilities are still resolved at 50Rc. Finally, we impose thermal inhomogeneities in order to pin the rolls, and show that the fluctuations are suppressed only if the local heat flux is a significant fraction of the convective heat transport per wavelength.