Research School of Earth Sciences, Australian National University, Canberra, Australian Capital Territory 0200, Australia.
Phys Rev Lett. 2013 Sep 20;111(12):124301. doi: 10.1103/PhysRevLett.111.124301. Epub 2013 Sep 17.
A new, more complete view of the mechanical energy budget for Rayleigh-Bénard convection is developed and examined using three-dimensional numerical simulations at large Rayleigh numbers and Prandtl number of 1. The driving role of available potential energy is highlighted. The relative magnitudes of different energy conversions or pathways change significantly over the range of Rayleigh numbers Ra ~ 10(7)-10(13). At Ra < 10(7) small-scale turbulent motions are energized directly from available potential energy via turbulent buoyancy flux and kinetic energy is dissipated at comparable rates by both the large- and small-scale motions. In contrast, at Ra ≥ 10(10) most of the available potential energy goes into kinetic energy of the large-scale flow, which undergoes shear instabilities that sustain small-scale turbulence. The irreversible mixing is largely confined to the unstable boundary layer, its rate exactly equal to the generation of available potential energy by the boundary fluxes, and mixing efficiency is 50%.
提出并研究了瑞利-贝纳德对流的机械能预算的新的、更完整的观点，使用三维数值模拟在大瑞利数和普朗特数为 1 的条件下进行。强调了可用势能的驱动作用。不同能量转换或途径的相对大小在瑞利数 Ra~10(7)-10(13)的范围内发生显著变化。在 Ra<10(7)时，小尺度湍流动能直接由可用势能通过湍流通量来激发，并且动能通过大尺度和小尺度运动以可比的速率耗散。相比之下，在 Ra≥10(10)时，大部分可用势能转化为大尺度流动的动能，大尺度流动经历剪切不稳定性，维持小尺度湍流。不可逆混合主要局限于不稳定的边界层，其速率恰好等于边界通量产生的可用势能，混合效率为 50%。
