AI 中文总结
研究可压缩湍流边界层中速度与温度场的雷诺类比问题，通过瞬时相似关系同时封闭平均场和脉动场，得出封闭关系且无自由参数，并精确恢复RSRA，经DNS数据验证，将其从经验关系转变为普遍性原理的结果。
AI 中文摘要
速度与温度场之间的雷诺类比是可压缩壁面湍流统计理论的核心问题。作者之前建立的广义雷诺类比（GRA）准确描述了平均速度 - 温度关系，但脉动场的自洽封闭仍未实现。本文表明瞬时相似关系，即广义总焓（减去其壁面值）与局部速度成比例，可同时封闭两个场。平均场再现了GRA解，脉动场得出封闭关系$T'_{rms}/u'_{rms} = |a_u^{-1/2}Pr^{-1/4}Pr_m^{-1/2}\,\partial\bar{T}/\partial\bar{u}|$，该关系源自三个普遍性：流向能量分数的通用结构常数$a_u$（约1.0 - 1.1）、生产与耗散的准平衡以及奥布霍夫 - 科尔辛截止尺度普遍性，且无自由参数。它精确恢复了Huang等人（2025）的精细强雷诺类比（RSRA），将其从经验关系重塑为普遍性原理的结果，并解释其拟合系数1.09为$a_u^{-1/2}Pr^{-1/4}$（对于$Pr = 0.71$，$a_u = 1.0$），并通过跨马赫数和壁面热条件的边界层直接数值模拟（DNS）数据验证，结果收敛到统一值。
英文摘要
The Reynolds analogy between velocity and temperature fields is a central problem in the statistical theory of compressible wall turbulence. The generalized Reynolds analogy (GRA) established by the author describes the mean velocity--temperature relation accurately, but a self-consistent closure for the fluctuating field has remained elusive. Here, the instantaneous similarity relation that the generalized total enthalpy (minus its wall value) is proportional to the local velocity is shown to close both fields at once. The mean field reproduces the GRA solution, while the fluctuating field yields the closed relation $T'_{rms}/u'_{rms} = f(Re_τ,\Pr)\,\Pr_m^{-1/2}\,|\partial\bar{T}/\partial\bar{u}|$, where the prefactor $f$ is derived from the universal cascade dynamics of turbulence and the Obukhov--Corrsin theory, without adjustable parameters. The relation recovers the refined strong Reynolds analogy (RSRA) of Huang et al.~(2025), the most accurate benchmark to date, recasting it from an empirical relation into a consequence of universality principles and explaining the origin of its fitted prefactor $f=1.09$; and its ratio to boundary-layer and channel direct numerical simulation (DNS) data collapses onto unity across Mach numbers ($2.25$--$14$), Prandtl numbers ($0.025$--$1$) and wall thermal conditions, with an overall accuracy of about $5\%$.
