论文标题
雷利 - 贝纳德对流的多尺度稳定解决方案
Multi-scale steady solution for Rayleigh-Bénard convection
论文作者
论文摘要
我们发现，通过使用来自Motoki等人给出的壁壁到壁最佳传输解决方案的同型，在水平板之间的三维周期板之间，在水平板之间的三维周期板之间，在水平板之间的三维周期性域中，在三维周期板之间进行了多尺度的稳定解。 （J. Fluid Mech。，第851卷，2018年，R4）。通过使用Newton-Krylov Iteration，可以跟踪连接的稳定稳定解决方案，这是雷利数字$ ra \ sim10^{3} $的分叉的结果。确切的相干热对流表现出缩放$ nu \ sim ra^{0.31} $（其中$ nu $是nusselt编号）以及多尺度的热羽和涡流结构，这些结构与湍流的rayleigh-bénard对流中非常相似。温度和速度波动的平均温度曲线和根平方与湍流状态的温度和速度波动非常吻合。此外，能量谱遵循Kolmogorov的-5/3缩放定律，并具有一致的预成分，并且在波数空间中的能量转移到较小的尺度与湍流能量传递一致。
We have found a multi-scale steady solution of the Boussinesq equations for Rayleigh-Bénard convection in a three-dimensional periodic domain between horizontal plates with a constant temperature difference by using a homotopy from the wall-to-wall optimal transport solution given by Motoki et al. (J. Fluid Mech., vol. 851, 2018, R4). The connected steady solution, which turns out to be a consequence of bifurcation from a thermal conduction state at the Rayleigh number $Ra\sim10^{3}$, is tracked up to $Ra\sim10^{7}$ by using a Newton-Krylov iteration. The exact coherent thermal convection exhibits scaling $Nu\sim Ra^{0.31}$ (where $Nu$ is the Nusselt number) as well as multi-scale thermal plume and vortex structures, which are quite similar to those in the turbulent Rayleigh-Bénard convection. The mean temperature profiles and the root-mean-square of the temperature and velocity fluctuations are in good agreement with those of the turbulent states. Furthermore, the energy spectrum follows Kolmogorov's -5/3 scaling law with a consistent prefactor, and the energy transfer to smaller scales in the wavenumber space agrees with the turbulent energy transfer.
