AI 中文总结
该研究针对湍流粗糙壁面压力谱，通过拆分压力源为不同部分，解释其方差随对数跨度增长的机制，建立了与雷诺数无关的模型，提出了无参数预测及验证方案。
AI 中文摘要
湍流边界层下方的壁面压力波动会驱动粗糙表面的流致噪声和结构载荷。在光滑壁面上，其方差随雷诺数的对数增长，根据源项解读，该增长由压力源的非线性湍流-湍流部分（作用于对数层）承载。我们探究当壁面完全粗糙时，是什么因素导致了相同的增长。标准粗糙壁面现象学给出了答案：在粗糙度上方，平均流保持其光滑壁面的对数形式，因此活跃源范围在粗糙度高度处而非粘性长度处被截断，方差随粗糙度高度与层厚度之间的对数跨度增长，取代了雷诺数。将压力源拆分为两个物理部分后，可区分对能量的不同贡献：来自平均剪切源的粗糙度局部贡献（在高频下固定于粗糙度尺度），以及来自外尺度非线性源的能量贡献（仅该贡献承载增长）。针对粗糙壁面案例校准后，该模型将谱形收敛至该能量峰，且在固定几何下与雷诺数无关。冠层贡献随离壁距离衰减，贡献有限偏移。预测增长系数为光滑壁面的增长系数，当前研究范围过窄，无法区分该系数与两倍或一半该系数的差异，因此该贡献为无参数预测，且需确定合适的粗糙度尺寸扫描来验证该预测。
英文摘要
Wall-pressure fluctuations beneath a turbulent boundary layer drive the flow-induced noise and structural loading of rough surfaces. On a smooth wall their variance grows with the logarithm of the Reynolds number, a growth carried, in a source-term reading, by the nonlinear turbulence--turbulence part of the pressure source acting across the logarithmic layer. We ask what sets the same growth once the wall is fully rough. Standard rough-wall phenomenology answers it: above the roughness the mean flow keeps its smooth-wall logarithmic form, so the active source range is cut off at the roughness height rather than the viscous length, and the variance grows on the logarithmic span between the roughness height and the layer thickness in place of the Reynolds number. Splitting the pressure source into its two physical parts then distinguishes separate contributions to the energy: a roughness-local one from the mean-shear source, fixed at high frequency on the roughness scale, and an energetic one from the nonlinear source at the outer scale, which alone carries the growth. Calibrated against rough-wall cases, the model collapses the spectral shape onto this energetic peak and holds it Reynolds-independent at fixed geometry. The canopy contribution decays with distance from the wall and contributes a finite offset. The growth coefficient is predicted to be the smooth-wall one. The present range is too narrow to discriminate that rate from twice or half it, so the contribution is a parameter-free prediction and the identification of a suitable roughness-size sweep that would test it.
