低普朗特数下均匀双扩散阶梯的通量
Fluxes through a uniform double-diffusive staircase at low Prandtl number
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中文总结 AI 辅助
本研究通过直接数值模拟探究低普朗特数下的双扩散阶梯，发现其可在更高密度比下存在，提出新存在判据与通量标度律，并建立基于界面密度异常混合的模型解释低Pr数据。
中文摘要 AI 辅助
扩散区的双扩散对流常观测到长寿命的分层状态，这一现象在北冰洋和火山湖中广为人知，且被认为存在于巨行星内部。其密度分布形似“阶梯”，由一系列密度均匀的对流层堆叠而成，层与层之间被强分层界面分隔。控制参数包括普朗特数$\text{Pr}$、扩散系数比$τ$、密度比$R_ρ$以及瑞利数$\text{Ra}$。本研究在三重周期域中开展直接数值模拟，系统探究了$τ\boldsymbol{\text{≤}} \text{Pr} \boldsymbol{\text{≪}} 1$条件下统计稳态双扩散阶梯的特性。研究证明，这类阶梯可在远大于此前报道的密度比条件下存在，并提出了长寿命分层状态存在的新判据。值得注意的是，该判据对$\text{Ra}$的依赖性较弱。在所有模拟中，我们测量了总密度通量$F^{\text{tot}}_ρ$、总温度通量$F^{\text{tot}}_T$和总成分通量$F^{\text{tot}}_C$，以及通量比$γ=F^{\text{tot}}_C/F^{\text{tot}}_T$。我们证实，在中等到较大的$R_ρ$范围内$γ$近似为常数，但也对$\text{Ra}$存在弱依赖性。研究表明，在此极限下成分和温度的努塞尔数满足$\text{Ra}^{1/3}$标度律，这与此前在较低$R_ρ$下发现的$(\text{RaPr})^{1/3}$标度律存在显著差异。我们基于界面边缘形成的密度异常的上升和湍流混合，提出了一个解释这些发现的新模型。该模型能以合理的精度解释现有的低$\text{Pr}$数据。
英文摘要
Double-diffusive convection in the diffusive regime is often observed to be in a long-lived layered state, well-known in the Arctic ocean and in volcanic lakes, and thought to exist in the interiors of giant planets. The density profile resembles a `staircase', with stacks of convective layers of uniform density separated by strongly stratified interfaces. The governing parameters are the Prandtl number $\mathrm{Pr}$, diffusivity ratio $τ$, density ratio $R_ρ$, and Rayleigh number $\mathrm{Ra}$. In this work, we perform direct numerical simulations in triply periodic domains to systematically investigate the properties of statistically stationary double-diffusive staircases with $τ\le \mathrm{Pr} \ll 1$. We demonstrate that they can exist for significantly larger density ratios than previously reported, and propose a new criterion for the existence of long-lived layered states. Notably, this criterion depends weakly on $\mathrm{Ra}$. In all simulations, we measure the total fluxes of density $F^{\mathrm{tot}}_ρ$, temperature $F^{\mathrm{tot}}_T$ and composition $F^{\mathrm{tot}}_C$, and the flux ratio $γ=F^{\mathrm{tot}}_C/F^{\mathrm{tot}}_T$. We confirm that $γ$ is approximately constant for moderate to large $R_ρ$ but also depends weakly on $\mathrm{Ra}$. We show that the Nusselt numbers for composition and temperature scale as $\mathrm{Ra}^{1/3}$ in this limit, which notably differs from the $(\mathrm{RaPr})^{1/3}$ scaling previously found at lower $R_ρ$. We propose a new model for these findings that is based on the rise and turbulent mixing of density anomalies that form at the edges of the interfaces. The model explains the existing low $\mathrm{Pr}$ data with reasonable accuracy.
发表机构
- University of California Santa Cruz（加州大学圣克鲁兹分校）
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