Toppaladoddi Srikanth, Succi Sauro, Wettlaufer John S
Yale University, New Haven, Connecticut 06520, USA.
Istituto per le Applicazioni del Calcolo "Mauro Picone" (C.N.R.), 00185 Rome, Italy.
Phys Rev Lett. 2017 Feb 17;118(7):074503. doi: 10.1103/PhysRevLett.118.074503. Epub 2017 Feb 16.
We use highly resolved numerical simulations to study turbulent Rayleigh-Bénard convection in a cell with sinusoidally rough upper and lower surfaces in two dimensions for Pr=1 and Ra=[4×10^{6},3×10^{9}]. By varying the wavelength λ at a fixed amplitude, we find an optimal wavelength λ_{opt} for which the Nusselt-Rayleigh scaling relation is (Nu-1∝Ra^{0.483}), maximizing the heat flux. This is consistent with the upper bound of Goluskin and Doering [J. Fluid Mech. 804, 370 (2016)JFLSA70022-112010.1017/jfm.2016.528] who prove that Nu can grow no faster than O(Ra^{1/2}) as Ra→∞, and thus with the concept that roughness facilitates the attainment of the so-called ultimate regime. Our data nearly achieve the largest growth rate permitted by the bound. When λ≪λ_{opt} and λ≫λ_{opt}, the planar case is recovered, demonstrating how controlling the wall geometry manipulates the interaction between the boundary layers and the core flow. Finally, for each Ra, we choose the maximum Nu among all λ, thus optimizing over all λ, to find Nu_{opt}-1=0.01×Ra^{0.444}.
我们使用高分辨率数值模拟来研究在二维情况下，普朗特数(Pr = 1)且瑞利数(Ra=[4×10^{6},3×10^{9}])时，具有正弦形粗糙上表面和下表面的单元中的湍流瑞利 - 贝纳德对流。通过在固定振幅下改变波长(\lambda)，我们找到了一个最优波长(\lambda_{opt})，对于该波长，努塞尔 - 瑞利标度关系为((Nu - 1∝Ra^{0.483}))，此时热通量最大。这与戈卢斯金和多林[《流体力学杂志》804, 370 (2016)JFLSA70022 - 112010.1017/jfm.2016.528]的上限一致，他们证明当(Ra→∞)时，(Nu)的增长速度不会超过(O(Ra^{1/2}))，因此与粗糙度有助于达到所谓极限状态的概念一致。我们的数据几乎达到了该边界允许的最大增长率。当(\lambda≪\lambda_{opt})和(\lambda≫\lambda_{opt})时，恢复到平面情况，这展示了如何通过控制壁面几何形状来操纵边界层与核心流之间的相互作用。最后，对于每个(Ra)，我们在所有(\lambda)中选择最大的(Nu)，从而在所有(\lambda)上进行优化，得到(Nu_{opt}-1 = 0.01×Ra^{0.444})。
