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arXiv 1908.10194physics.flu-dyn
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分形表面上的热对流

Thermal Convection over Fractal Surfaces

Srikanth Toppaladoddi, Andrew J. Wells, Charles R. Doering, John S. Wettlaufer

备注：
15 pages, 13 figures
发表信息：
J. Fluid Mech. 907 (2021) A12
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摘要：

我们采用格子Boltzmann方法对二维$Pr = 1$和$Ra \in \left[10^7, 10^{10}\right]$的分形边界单元中的Rayleigh-Bénard对流进行了数值模拟。分形边界是以功率谱密度$S(k)$为特征的函数，其随波数$k$衰减为$S(k) \sim k^{p}$（$p < 0$）。粗糙度由指数$p$量化，其中$p < -3$用于光滑（可微）表面，$-3 \le p < -1$用于具有Hausdorff维数$D_f=\frac{1}{2}(p+5)$的粗糙表面。通过计算幂律中的指数$β$拟合$Nu \sim Ra^β$，其中$Nu$和$Ra$是$Ra \in \left[10^8, 10^{10}\right]$的Nusselt数和Rayleigh数，我们观察到热传输标度随着$Ra \in \left[10^8, 10^{10}\right]$的前二十年的粗糙度而增加。对于$p$ $= -3.0$、$-2.0$和$-1.5$，我们分别找到了$β= 0.288 \pm 0.005, 0.329 \pm 0.006$和$0.352 \pm 0.011$。我们还观察到，雷诺数$Re$与$Re \sim Ra^ξ$成比例，其中$ξ\approx 0.57$超过$Ra \in \left[10^7, 10^{10}\right]$，对于研究中使用的所有$p$。对于给定的$p$值，平均$Nu$和$Re$对粗糙度的具体实现不敏感。

英文摘要：

We use well resolved numerical simulations with the Lattice Boltzmann Method to study Rayleigh-Bénard convection in cells with a fractal boundary in two dimensions for $Pr = 1$ and $Ra \in \left[10^7, 10^{10}\right]$. The fractal boundaries are functions characterized by power spectral densities $S(k)$ that decay with wavenumber, $k$, as $S(k) \sim k^{p}$ ($p < 0$). The degree of roughness is quantified by the exponent $p$ with $p < -3$ for smooth (differentiable) surfaces and $-3 \le p < -1$ for rough surfaces with Hausdorff dimension $D_f=\frac{1}{2}(p+5)$. By computing the exponent $β$ in power law fits $Nu \sim Ra^β$, where $Nu$ and $Ra$ are the Nusselt and the Rayleigh numbers for $Ra \in \left[10^8, 10^{10}\right]$, we observe that heat transport scaling increases with roughness over the top two decades of $Ra \in \left[10^8, 10^{10}\right]$. For $p$ $= -3.0$, $-2.0$ and $-1.5$ we find $β= 0.288 \pm 0.005, 0.329 \pm 0.006$ and $0.352 \pm 0.011$, respectively. We also observe that the Reynolds number, $Re$, scales as $Re \sim Ra^ξ$, where $ξ\approx 0.57$ over $Ra \in \left[10^7, 10^{10}\right]$, for all $p$ used in the study. For a given value of $p$, the averaged $Nu$ and $Re$ are insensitive to the specific realization of the roughness.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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