Rotating turbulent thermal convection at large Rayleigh numbers

在这个项目中，我们将通过实验和数值模拟的互补工作来研究非常大瑞利数Ra的旋转湍流Rayleigh-Benard对流(RBC)。虽然我们在实验中精确地测量了Ra到1e15的对流热传输，但模拟提供了关于内部流动结构的任何所需的详细程度。为了在实验上达到如此高的Ra，我们将使用压缩到19bar的六氟化硫作为对流流体，导致普朗特数(Pr)约为0.8。用反Rossby数(1/Ro)表示的最大自转速度约为20。其中一项主要研究考虑了自转对向最终RBC状态转变的影响。由于假设Ra的最终状态占上风，我们预计我们的实验室结果将合理地外推到与地球和天体物理相关的Ra和1/Ro范围。另一项初步研究将讨论地转区域内的热量输送和流动结构。这是在非常高的Ra和1/Ro时的情况，当压力梯度被科里奥利力平衡时，科里奥利力在地球大气中占主导地位。直接数值模拟(DNS)将对Ra到1e11进行，具有与实验中相同的对流单体几何形状、相同的1/Ro范围和相似的Pr。在数值研究中，我们特别想要研究Ekman和Stewartson边界层的结构和动力学，全球流动结构及其与环极能量平衡的密切联系，以及速度和温度波动。同样，通过数值计算，我们的目标是探索地转湍流的机制。事实上，在参数空间中，对于Ra从1e9到1e11和1/Ro从0.02到20，有一个区域，其中实验和Dns重叠，并且至少在某些部分预期有地转条件。在实验和数值计算的共同作用下，我们将对更好地理解旋转红细胞在这种情况下的流场和热输运特性做出重要贡献。

With the proposed project we will study rotating turbulent Rayleigh-Benard convection (RBC) at very large Rayleigh numbers Ra by complementary efforts from experiments and numerical simulations. While we measure accurately the convective heat transport in the experiment for Ra up to 1e15, the simulations provide any desired level of detail about the internal flow structure. In order to reach such high Ra experimentally, we will use compressed sulfur hexafloride at up to 19 bar as the convecting fluid, resulting in a Prandtl number (Pr) of about 0.8. The maximal rotation rate as expressed by the inverse Rossby number (1/Ro) will be about 20. One of the primary investigations considers the influence of rotation on the transition to the ultimate RBC state. As the ultimate state is assumed to prevail for diverging Ra, we expect a reasonable extrapolation of our laboratory results to the geo- and astrophysically relevant ranges of Ra and 1/Ro. Another primary investigation will address the heat transport and the flow structure in the geostrophic regime. That is the regime at very high Ra and 1/Ro when pressure gradients are balanced by Coriolis forces, which is dominant in the earth's atmosphere.Direct Numerical Simulations (DNS) will be conducted for Ra up to 1e11 with the same geometry of the convection cell, the same 1/Ro-range, and similar Pr as in the experiment. In the numerical investigations, we in particular want to study the structure and dynamics of the Ekman and Stewartson boundary layers, the global flow structures and their close connection to the toroidal-poloidal energy balance, and the velocity and temperature fluctuations. Also with the numerics, we aim to explore the regime of geostrophic turbulence. In fact there is a region in the parameter space, for Ra from 1e9 to 1e11 and 1/Ro from 0.02 to 20, where experiments and DNS overlap, and where at least in some parts geostrophic conditions are expected. With the complementary efforts from both experiment and numerics, we will significantly contribute for a better understanding of the flow field and the heat transport properties in rotating RBC in this regime.