Internally heated convection

热驱动湍流在自然界和技术中无处不在。它们的发生是由于在对流单元的边界处设置的特定热条件和/或由于单元内的内部热源。在这个项目中，我们将研究湍流热对流与后一种形式的驱动-即内部加热驱动，无论是经典的情况下，恒定的驱动和空间和时间调制的驱动，这是更接近内部加热湍流的许多应用。我们结合的理论和数值研究将基于二维和三维直接数值模拟，这将在广泛的控制参数范围内进行：高达五十年的普朗特数，高达六十年的瑞利-罗伯茨数，高达四十年的热调制频率。 首先，对于恒定的热驱动，通过直接数值模拟，我们将验证并进一步发展内部加热对流中动量输运（雷诺数）和体温度的标度理论。基于在广泛的参数范围内对数值数据的深入分析，我们将扩展标度理论，以预测通过流体层的任何水平表面（包括顶部和底部）的热传输，即相应的努塞尔数，在内部加热对流中，它取决于与底板的距离。我们还将揭示全球流动响应参数与局部流动组织之间的联系。特别是，我们将扩展边界层理论所考虑的热对流类型，并从扩展的边界层方程推导出速度和温度的垂直平均分布。内部加热流体层的上部、浮力占主导地位的部分和下部、穿透部分的流动结构和剖面是完全不同的。 最后，时间和时空调制的内部加热湍流对流的后果将进行研究。特别是，我们要了解的热驱动源的空间和/或时间调制的全球流动组织，热量和动量的传输，以及系统的整体温度的影响。 我们希望根据调制频率识别不同的机制，并希望从理论上解释这些机制以及它们之间的过渡。

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.