Vincent A P, Yuen D A
Département de Physique, Université de Montréal C.P. 6128, Succursale A, Montréal, Québec, Canada H3C 3J7.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Sep;60(3):2957-63. doi: 10.1103/physreve.60.2957.
We have conducted a high-resolution, two-dimensional direct numerical simulation of Rayleigh-Bénard convection with stress-free and periodic boundary conditions at a Rayleigh (Ra) number of 10(8) and Prandtl (Pr) number of unity. An aspect-ratio three box has been considered. A single cell has been used as the initial condition. First, the flow develops into time-dependent convection with a strong asymmetry and highly convoluted thermal plumes delineating a large-scale circulation. Smaller thermal plumes detach from the boundary layer and extend over the entire cell, creating a local inversion of the temperature gradient adjacent to the boundary layers. Then the conditions leading to the formation of internal waves are fulfilled, as the local Richardson number decreases sufficiently small to cross the linear threshold of Ri=0.25. Together with the strong shear, convective rolls with a Kelvin-Helmholtz wavelike character are produced. The secondary boundary layer itself becomes unstable and produces smaller plumes. At later times, the large-scale circulation is destroyed and the internal waves disappear. A Reynolds number, based on the global scale, of Re=500, is attained at this stage. Only isolated thermal plumes and vortices are present. Thus, internal waves can be generated at finite Prandtl number fluids for sufficiently high Ra in the presence of a large-scale circulation. Spectral analysis reveals that the kinetic energy decays with a logarithmic slope of -3, while the logarithmic slope of the thermal variance has a value of around -5 / 3.
我们在瑞利数（Ra）为10⁸、普朗特数（Pr）为1的情况下，对具有无应力和周期性边界条件的瑞利 - 贝纳德对流进行了高分辨率二维直接数值模拟。考虑了长宽比为3的盒子。初始条件采用单个单元。首先，流动发展为具有强烈不对称性和高度复杂热羽流的时间相关对流，描绘出一个大尺度环流。较小的热羽流从边界层脱离并延伸到整个单元，在边界层附近产生温度梯度的局部反转。然后，随着局部理查森数减小到足够小以越过Ri = 0.25的线性阈值，导致内波形成的条件得以满足。连同强烈的剪切作用，产生具有开尔文 - 亥姆霍兹波状特征的对流涡旋。二次边界层本身变得不稳定并产生较小的羽流。在后期，大尺度环流被破坏，内波消失。在此阶段，基于全局尺度的雷诺数Re = 500得以实现。此时仅存在孤立的热羽流和涡旋。因此，在存在大尺度环流的情况下，对于足够高的Ra，有限普朗特数流体中可以产生内波。频谱分析表明，动能以-3的对数斜率衰减，而热方差的对数斜率约为-5 / 3。
