Tandon School of Engineering, New York University, New York, NY 11201.
Department of Physics, Occidental College, Los Angeles, CA 90041.
Proc Natl Acad Sci U S A. 2020 Apr 7;117(14):7594-7598. doi: 10.1073/pnas.1922794117. Epub 2020 Mar 25.
The global transport of heat and momentum in turbulent convection is constrained by thin thermal and viscous boundary layers at the heated and cooled boundaries of the system. This bottleneck is thought to be lifted once the boundary layers themselves become fully turbulent at very high values of the Rayleigh number [Formula: see text]-the dimensionless parameter that describes the vigor of convective turbulence. Laboratory experiments in cylindrical cells for [Formula: see text] have reported different outcomes on the putative heat transport law. Here we show, by direct numerical simulations of three-dimensional turbulent Rayleigh-Bénard convection flows in a slender cylindrical cell of aspect ratio [Formula: see text], that the Nusselt number-the dimensionless measure of heat transport-follows the classical power law of [Formula: see text] up to [Formula: see text] Intermittent fluctuations in the wall stress, a blueprint of turbulence in the vicinity of the boundaries, manifest at all [Formula: see text] considered here, increasing with increasing [Formula: see text], and suggest that an abrupt transition of the boundary layer to turbulence does not take place.
在热对流中，热量和动量的全球传输受到系统加热和冷却边界处薄的热和粘性边界层的限制。一旦边界层本身在瑞利数[Formula: see text]（描述对流湍流强度的无量纲参数）非常高的值下变得完全湍流，这种瓶颈就被认为会被消除。在圆柱胞中针对[Formula: see text]的实验室实验报告了关于假定的热输运定律的不同结果。在这里，我们通过对高宽比[Formula: see text]的细长圆柱胞中三维湍流传热的直接数值模拟表明，努塞尔数（无量纲热输运量）遵循经典的[Formula: see text]幂律，直至[Formula: see text]。在所有考虑的[Formula: see text]中，边界附近湍流的蓝图——壁面应力的间歇性波动都明显增加，随着[Formula: see text]的增加而增加，这表明边界层向湍流的突然转变不会发生。
