Convection planforms in a fluid with a temperature‐dependent viscosity beneath a stress‐free upper boundary

Abstract

This study presents the results of a joint numerical and laboratory study of 3‐D planforms of time‐dependent convection in a Newtonian fluid layer with a temperature‐dependent viscosity. Planforms are found for the case in which the fluid is bounded from above by a stress‐free boundary and below by a rigid boundary and compared to the planforms found when the fluid layer is bounded by rigid boundaries. All of the laboratory and numerical experiments were performed with nearly the same values of the Rayleigh number Ra1/2 (1 × 105) and viscosity ratio µr (50), and viscosity law to allow direct comparisons. When the fluid layer is bounded by rigid boundaries the observed planforms are the spoke patterns, which are an interconnected network of descending and ascending sheets. However, when the upper boundary is stress‐free, the morphology of the downwellings change from spokes to a dendritic network of descending sheets and the wavelength of the planform is more than 3 times as large as the spoke pattern planform. In both cases the numerical and laboratory experiments are in good agreement.