论文标题
冷却箱问题：带有二次状态方程的对流
The Cooling Box Problem: Convection with a quadratic equation of state
论文作者
论文摘要
我们通过对具有固定顶部温度的流量进行三维直接数值模拟，研究具有二维状态的流体对流冷却，该模拟低于初始流体温度。我们认为在最高密度的最高密度接近，预计非线性很重要。当状态方程为非线性时，最终的热的垂直转运根本不同，并且明显低于对状态线性方程的预测。此外，三个无量纲组的参数化对流系统：瑞利号（$ \ hbox {ra} _0 $），prandtl编号（pr）和无量纲的底部水温$（t_b）$。我们进一步定义了一个有效的瑞利号（$ \ hbox {ra} _ {eff} = ra_0 \ t_b^2 $），这等同于与状态线性方程式使用的传统雷利号。我们提出了垂直热通量，顶部边界层厚度和系统湍流动能的预测模型。我们表明，该模型与直接数值模拟非常吻合。该模型可用于了解在高纬度环境中淡水湖凉爽的速度。
We investigate the convective cooling of a fluid with a quadratic equation of state by performing three-dimensional direct numerical simulations of a flow with a fixed top-boundary temperature, which is lower than the initial fluid temperature. We consider fluid temperatures near the density maximum, where the nonlinearity is expected to be important. When the equation of state is nonlinear, the resultant vertical transport of heat is fundamentally different and significantly lower than the predictions derived for a linear equation of state. Further, three dimensionless groups parameterize the convective system: the Rayleigh number ($\hbox{Ra}_0$), the Prandtl number (Pr), and the dimensionless bottom water temperature $(T_B)$. We further define an effective Rayleigh number ($\hbox{Ra}_{eff} = Ra_0 \ T_B^2$), which is equivalent to the traditional Rayleigh number used with a linear equation of state. We present a predictive model for the vertical heat flux, the top boundary-layer thickness, and the turbulent kinetic energy of the system. We show that this model agrees well with the direct numerical simulations. This model could be used to understand how quickly freshwater lakes cool in high latitude environments.
