Department of Applied Mathematics and Statistics, Jack Baskin School of Engineering, University of California Santa Cruz, 1156 High Street, Santa Cruz, California 95064, USA.
Phys Rev E. 2017 Sep;96(3-1):033104. doi: 10.1103/PhysRevE.96.033104. Epub 2017 Sep 11.
We examine the dynamics associated with weakly compressible convection in a spherical shell by running 3D direct numerical simulations using the Boussinesq formalism [Spiegel and Veronis, Astrophys. J. 131, 442 (1960)AJLEEY0004-637X10.1086/146849]. Motivated by problems in astrophysics, we assume the existence of a finite adiabatic temperature gradient ∇T_{ad} and use mixed boundary conditions for the temperature with fixed flux at the inner boundary and fixed temperature at the outer boundary. This setup is intrinsically more asymmetric than the more standard case of Rayleigh-Bénard convection in liquids between parallel plates with fixed temperature boundary conditions. Conditions where there is substantial asymmetry can cause a dramatic change in the nature of convection and we demonstrate that this is the case here. The flows can become pressure- rather than buoyancy-dominated, leading to anomalous heat transport by upflows. Counterintuitively, the background temperature gradient ∇T[over ¯] can develop a subadiabatic layer (where g·∇T[over ¯]<g·∇T_{ad}, where g is gravity) although convection remains vigorous at every point across the shell. This indicates a high degree of nonlocality.
我们通过使用 Boussinesq 公式运行 3D 直接数值模拟来研究球形壳中与弱可压缩对流相关的动力学[Spiegel 和 Veronis，Astrophys. J. 131, 442 (1960)AJLEEY0004-637X10.1086/146849]。受天体物理学问题的启发，我们假设存在有限的绝热温度梯度∇T_{ad}，并对内边界使用温度混合边界条件，通量固定，对外边界使用温度固定。与平行板之间具有固定温度边界条件的更标准的瑞利-贝纳尔对流相比，这种设置本质上更不对称。存在大量不对称的条件会导致对流性质发生剧烈变化，我们证明了这里就是这种情况。流动可能会受到压力而不是浮力的控制，从而导致上升流异常的热传输。与直觉相反，尽管在整个壳层的每一点上对流仍然很剧烈，但背景温度梯度∇T[over ¯]可能会发展出亚绝热层（其中 g·∇T[over ¯]<g·∇T_{ad}，其中 g 是重力）。这表明存在高度的非局部性。
