In this paper, a simple method to locally compute the model coefficient \(C_{DES}\) in Reddy et al. (Int J Heat Fluid Flow 50:103–113, 2014. https://doi.org/10.1016/j.ijheatfluidflow.2014.06.002) is presented. The formula for the coefficient is derived from the structural function \(B_{\beta }\) of Vreman (Phys Fluids 16(10):3670–3681, 2004. https://doi.org/10.1063/1.1785131). It, therefore, does not involve explicit filtering or averaging procedures. By virtue of the variable coefficient being based on \(B_{\beta }\), the model is expected to retain the property of relatively small dissipation in transitional and near-wall regions. This property enables the present formulation to be a reasonable candidate to predict transitional flows. The formulation is validated in the canonical, fully developed turbulent channel and backward facing step flows, followed by simulations of orderly, bypass and separation induced laminar-to-turbulent transition in a spatially developing boundary layer over a flat plate.

在本文中，Reddy 等人提出了一种本地计算模型系数\(C_{DES}\)的简单方法。(Int J Heat Fluid Flow 50:103–113, 2014. https://doi.org/10.1016/j.ijheatfluidflow.2014.06.002)。系数的公式源自Vreman的结构函数\(B_{\beta }\)（Phys Fluids 16(10):3670–3681, 2004. https://doi.org/10.1063/1.1785131）。因此，它不涉及显式过滤或平均过程。由于可变系数基于\(B_{\beta }\)，该模型有望保留在过渡和近壁区域中耗散相对较小的特性。这种特性使本公式成为预测过渡流的合理候选者。该公式在规范的、完全发展的湍流通道和后向阶梯流中得到验证，然后在平板上空间发展的边界层中模拟有序、旁路和分离引起的层流到湍流的转变。