论文标题
穿透性动荡的雷利 - 贝纳德对流的通用性能在冷水中靠近$ 4^\ circ \ rm {c} $
Universal properties of penetrative turbulent Rayleigh--Bénard convection in cold water near $4^\circ\rm{C}$
论文作者
论文摘要
在对流不稳定的流体层中发生的穿透性湍流是在数值和理论上渗透到相邻的，最初稳定分层的层的。我们选择了最相关的例子，即温度约为$ t_m \ y 4^\ circ \ rm {c} $的热驱动的水流量，其中它具有最大密度。我们选择带有底板温度$ T_B> 4^\ circ \ rm {c} $的雷利 - 贝纳德几何形状和顶板温度$ t_t \ le 4^\ circ \ rm {c} $。除了温度差设置的整体热驱动强度之外，$δ= t_b -t_t $（无量纲形式的瑞利号$ ra $），与标准的雷利 - 贝纳德对流相比，关键的新控制参数是密度反转参数$θ_m\ equiv（t_m -t_m -t_t） /δ$。至关重要的响应参数是相对平均中期温度$θ_c$和整体传热（即Nusselt Numbesl Number $ NU $）。从理论上讲，我们得出通用（即$ ra $ - 独立）依赖性$θ_c（θ_m）=（1+θ_m^2）/2 $，该$ $θ_m$以下$ ra $ a $ c的关键价值低于$ ra $依赖的关键价值$θ_m=θ_{m，c} $。我们的直接数值模拟，$ ra $最高$ 10^{10} $与这些结果一致。临界密度反转参数$θ_{m，c} $可以通过线性稳定性分析来精确预测。热通量$ nu（θ_m）$单调降低，随着$θ_m$的增加，我们可以从理论上得出相对热量$ nu（θ_m）/nu（0）$的通用关系。最后，我们在数值上识别并讨论了大$θ_m$之间不同湍流状态之间的罕见过渡。
Penetrative turbulence, which occurs in a convectively unstable fluid layer and penetrates into an adjacent, originally stably stratified layer, is numerically and theoretically analyzed. We chose the most relevant example, namely thermally driven flow of water with a temperature around $T_m\approx 4^\circ\rm{C}$, where it has its density maximum. We pick the Rayleigh-Bénard geometry with the bottom plate temperature $T_b > 4^\circ\rm{C}$ and the top plate temperature $T_t \le 4^\circ\rm{C}$. Next to the overall thermal driving strength set by the temperature difference $Δ= T_b - T_t$ (the Rayleigh number $Ra$ in dimensionless form), the crucial new control parameter as compared to standard Rayleigh-Bénard convection is the density inversion parameter $θ_m \equiv (T_m - T_t ) / Δ$. The crucial response parameters are the relative mean mid-height temperature $θ_c$ and the overall heat transfer (i.e., the Nusselt number $Nu$). We theoretically derive the universal (i.e., $Ra$-independent) dependence $θ_c (θ_m) =(1+θ_m^2)/2$, which holds for $θ_m$ below a $Ra$-dependent critical value, beyond which $θ_c (θ_m)$ sharply decreases and drops down to $θ_c=1/2$ at $θ_m=θ_{m,c}$. Our direct numerical simulations with $Ra$ up to $10^{10}$ are consistent with these results. The critical density inversion parameter $θ_{m,c}$ can be precisely predicted by a linear stability analysis. The heat flux $Nu(θ_m)$ monotonically decreases with increasing $θ_m$ and we can theoretically derive a universal relation for the relative heat flux $Nu(θ_m)/Nu(0)$. Finally, we numerically identify and discuss rare transitions between different turbulent flow states for large $θ_m$.
