The limitations of turbulence closure models in the context of Reynolds-averaged NavierStokes (RANS) simulations play a significant part in contributing to the uncertainty of Computational Fluid Dynamics (CFD). Perturbing the spectral representation of the Reynolds stress tensor within physical limits is common practice in several commercial and open-source CFD solvers, in order to obtain estimates for the epistemic uncertainties of RANS turbulence models. Recent research revealed, that there is a need for moderating the amount of perturbed Reynolds stress tensor tensor to be considered due to upcoming stability issues of the solver. In this paper we point out that the consequent common implementation can lead to unintended states of the resulting perturbed Reynolds stress tensor. The combination of eigenvector perturbation and moderation factor may actually result in moderated eigenvalues, which are not linearly dependent on the originally unperturbed and fully perturbed eigenvalues anymore. Hence, the computational implementation is no longer in accordance with the conceptual idea of the Eigenspace Perturbation Framework. We verify the implementation of the conceptual description with respect to its self-consistency. Adequately representing the basic concept results in formulating a computational implementation to improve self-consistency of the Reynolds stress tensor perturbation

翻译：湍流封闭模型在雷诺平均纳维-斯托克斯（RANS）模拟中的局限性，是导致计算流体动力学（CFD）不确定性的重要因素之一。在物理限制内扰动雷诺应力张量的谱表示，已成为多个商用和开源CFD求解器中估算RANS湍流模型认知不确定性的常用做法。近期研究表明，由于求解器可能出现稳定性问题，需要对扰动雷诺应力张量的幅度进行适度调节。本文指出，当前通用的实现方式可能导致最终扰动雷诺应力张量出现非预期状态。特征向量扰动与调节因子的组合可能生成调节后的特征值，这些特征值不再与原始未扰动和完全扰动的特征值保持线性相关关系。因此，计算实现已不再符合特征空间扰动框架的核心理念。我们针对该概念描述的计算实现进行了自洽性验证。正确表达基本概念后，我们提出了一种改进的计算实现方案，以增强雷诺应力张量扰动的自洽性。