PATTERN FORMATION IN CONVECTIVE INSTABILITIES

The present article reviews recent progress in the study of pattern formation in convective instabilities. After a brief discussion of the relevant basic hydrodynamic equations as well as a short outline of the mathematical treatment of pattern formation in complex systems the self-organization of spatial and spatio-temporal structures due to convective instabilities is considered. The formation of various forms of convective patterns arising in the Bénard experiment, i.e. in a horizontal fluid layer heated from below, is discussed. Then the review considers pattern formation in the Bénard instability in spherical geometries. In that case it can be demonstrated how the interaction among several convective cells may lead to time dependent as well as chaotic evolution of the spatial structures. Finally, the convective instability in a binary fluid mixture is discussed. In contrast to the instability in a single component fluid the instability may be oscillatory. In that case convection sets in in the form of travelling wave patterns which in addition to a complicated and chaotic temporal behaviour exhibit more or less spatial irregularity already close to threshold.