Internally heated convection

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Thermally driven turbulent flows are omnipresent in nature and technology. They occur due to specific thermal conditions set at the boundaries of a convection cell and/or due to internal sources of heat inside the cell. In this project, we will study turbulent thermal convection with this latter form of driving - namely, driving by internal heating, both for the classical case with constant driving and for spatially and temporally modulated driving, which is closer to many applications of internally heated turbulence. Our combined theoretical and numerical study will be based on two- and three-dimensional direct numerical simulations, which will be conducted in a broad range of control parameters: up to five decades in Prandtl number, up to six decades in Rayleigh--Roberts number, and up to four decades in the thermal modulation frequency. First, for constant thermal driving, with the direct numerical simulations, we will verify and further develop the scaling theory for the momentum transport (Reynolds number) and bulk temperature in internally heated convection. Based on a deep analysis of the numerical data in a broad parameter range, we will then extend the scaling theory to also predict the heat transport through any horizontal surface (including top and bottom) of the fluid layer, i.e. the corresponding Nusselt numbers, which in internally heated convection depend on the distance from the bottom plate. We will also reveal the connection between the global flow response parameters with the local flow organization. In particular, we will extend the boundary layer theory to the considered type of thermal convection and derive the vertical mean profiles of the velocity and of the temperature from the extended boundary layer equations. The structure of the flow and the profiles are quite different for the upper, buoyancy-dominated part of the internally heated fluid layer, and the lower, penetrative part. Finally, the consequences of temporally and spatiotemporally modulating the internally heated turbulent convection will be studied. In particular, we want to understand the effect of the spatial and/or temporal modulation of the thermal driving source on the global flow organization, the heat and momentum transport, and the bulk temperature of the system. We expect to identify different regimes, depending on the modulation frequency, and want to theoretically explain these regimes and the transitions between them.