Abstract The paper formulates a new derivation procedure for the standard elliptic relaxation turbulence model in the context of stratified flows. It begins with the introduction of an additional length scale for the buoyancy. A Taylor series expansion of the terms in the integral for the pressure-strain correlation paves the way for the formulation of an equivalent length scale as an explicit function of the integral length scale and the buoyancy length scale. The advantages of such an approach over previous research in the literature are two-fold: firstly, the number of elliptic relaxation equations is reduced by at least half thus making the model more practical and secondly, the same set of equations is valid for both stable and unstable stratification. The study forsakes elliptic relaxation for the scalar fluxes due to its emphasis on reducing computational complexity. The model predictions agree well with Direct Numerical Simulation (DNS) results available in the literature for both stably and unstably stratified flows at a range of stratification levels.

中文翻译：

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具有分层流的新椭圆松弛程序的雷诺应力模型

摘要 本文提出了分层流背景下标准椭圆松弛湍流模型的新推导程序。它首先为浮力引入了一个额外的长度尺度。压力-应变相关性积分项的泰勒级数展开为将等效长度标度公式化为积分长度标度和浮力长度标度的显式函数铺平了道路。与以往文献研究相比，这种方法的优点有两个：首先，椭圆松弛方程的数量减少了至少一半，从而使模型更实用；其次，同一组方程对于稳定的和不稳定的分层。该研究放弃了标量通量的椭圆弛豫，因为它强调降低计算复杂性。模型预测与文献中可用的直接数值模拟 (DNS) 结果非常吻合，适用于一系列分层水平的稳定和不稳定分层流。