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努力来研究在非常大的瑞利数Ra下旋转湍流瑞利-贝纳德对流（RBC）。虽然我们在实验中精确测量了Ra至1e15的对流热传输，但模拟提供了有关内部流动结构的任何所需的细节水平。为了在实验中达到如此高的Ra，我们将使用高达19 bar的压缩六氟化硫作为对流流体，得到约0.8的普朗特数（Pr）。用逆罗斯比数（1/Ro）表示的最大旋转速率约为20。其中一项初步研究考虑了旋转对最终RBC状态转变的影响。由于假设最终状态在Ra发散时占上风，我们期望将我们的实验室结果合理地外推到Ra和1/Ro的地球和天体物理相关范围。另一项主要研究将涉及地转状态下的热传输和流动结构。这是在非常高的Ra和1/Ro时，压力梯度由科里奥利力平衡的情况，科里奥利力在地球大气中占主导地位。采用与实验相同的对流池几何形状、相同的1/ o范围和相似的Pr，对Ra至1e11进行直接数值模拟（DNS）。在数值研究中，我们特别想研究Ekman和Stewartson边界层的结构和动力学，全球流动结构及其与环形-极向能量平衡的密切联系，以及速度和温度波动。同样，通过数值，我们旨在探索地转湍流的状态。事实上，在参数空间中存在一个区域，Ra从1e9到1e11, 1/Ro从0.02到20，实验和DNS重叠，并且至少在某些部分预计会出现地转条件。通过实验和数值的互补努力，我们将为更好地理解在这种情况下旋转RBC的流场和热输运特性做出重大贡献。

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.