In 1-equation URANS models of turbulence the eddy viscosity is given by $\nu_{T}=0.55l(x,t)\sqrt{k(x,t)}$ . The length scale $l$ must be pre-specified and $k(x,t)$ is determined by solving a nonlinear partial differential equation. We show that in interesting cases the spacial mean of $k(x,t)$ satisfies a simple ordinary differential equation. Using its solution in $\nu_{T}$ results in a 1/2-equation model. This model has attractive analytic properties. Further, in comparative tests in 2d and 3d the velocity statistics produced by the 1/2-equation model are comparable to those of the full 1-equation model.

翻译：在单方程URANS湍流模型中，涡粘性由$\nu_{T}=0.55l(x,t)\sqrt{k(x,t)}$给出。长度尺度$l$需预先设定，而$k(x,t)$通过求解非线性偏微分方程确定。研究表明，在典型工况下，$k(x,t)$的空间平均值满足一个简单的常微分方程。将其解代入$\nu_{T}$即获得1/2方程模型。该模型具有良好的解析性质。此外，在二维与三维对比测试中，1/2方程模型产生的速度统计量与完整单方程模型的结果相当。