Effects of variable thermal diffusivity on the structure of convection

The multiscale flow structure in the solar convection zone - the coexistence of such features as the granules, mesogranules, supergranules and giant cells - has not yet been properly understood. Here, the possible role of one physical factor - variations in the thermal diffusivity - in the formation of a multiscale convection structure is investigated. Thermal convection in a plane horizontal fluid layer is numerically simulated. The temperature dependence of thermal diffusivity is chosen so as to produce a sharp kink in the static temperature profile near the upper layer boundary. As a result, the magnitude of the (negative) static temperature gradient dTs/dz, being small over the most part of the layer thickness, reaches large values in a thin boundary sublayer. To identify the structures on different scales, we apply a smoothing procedure, computational-homology techniques and spectral processing to the temperature field. The flow is found to be a superposition of three cellular structures with three different characteristic scales. The largest (first-scale) convection cells, with central upflows, fill the whole layer thickness; most of these cells are divided by bridges, or isthmuses, into a few smaller (second-scale) ones, which are localised in the upper portion of the layer; finally, there are numerous tiny (third-scale) features that dot the horizontal sections of the layer located near its upper boundary and exhibit a tendency of gathering in the intercellular lanes of the first-scale cells. The third-scale cellular structures are advected by the first-scale and second-scale convective flows. The spatial spectrum of the flow does not directly indicate the presence of the second-scale and third-scale structures; however, they can be selected by using our processing techniques. On the whole, the simulated flow pattern qualitatively resembles that observed on the Sun.