This paper experimentally examined a feedback-loop mechanism generating tonal noise when a two-dimensional (2-D) protuberance as high as the boundary-layer thickness was placed in zero- and weak adverse-pressure-gradient laminar boundary layers. Onset of tonal noise required rapid disturbance growth due to strong instability in a small separation bubble formed just upstream of the protuberance, in addition to slow but long-distance amplification of Tollmien–Schlichting (T–S) waves in a 2-D form. The experiments clearly showed that the adverse pressure gradient, even if weak, appreciably affected amplification of T–S waves, and consequently reduced the threshold height of protuberance for the onset of tonal noise significantly. The result was supported by stability analyses (based on the PSE) of the boundary layers with and without a protuberance. The $N$-factor was found to be 11–12 for the threshold protuberance height in both boundary layers, which was large enough for T–S waves to evolve into strong vortices. When an additional receptivity region other than the leading edge region was introduced by gluing a thin 2-D roughness element much thinner than the boundary-layer displacement thickness at a location beyond the critical Reynolds number for linear instability, the threshold protuberance height decreased below 60% of the value in the absence of the roughness element. The frequencies of multiple discrete tones were explained by a simple feedback-loop model similar to the case of trailing-edge noise, assuming that the feedback-loop was established between the receptivity location and protuberance.

本文实验性地研究了当零边界层和薄弱的逆压梯度层边界层中放置一个二维边界（2-D），其边界层厚度高时，会产生音调噪声的反馈回路机制。声调噪声的发作需要快速的扰动增长，这是由于在隆起的上游形成的小分离气泡中存在强烈的不稳定性，另外还有二维形式的Tollmien-Schlichting（TS）波的缓慢但远距离的放大。实验清楚地表明，即使压力较弱，其不利的压力梯度也会显着影响T–S波的放大，从而显着降低了声调噪声起伏的阈值高度。带有和不带有隆起的边界层的稳定性分析（基于PSE）都支持该结果。$ñ$在两个边界层中，阈值突出高度的最大因子为11–12，该因子足够使T–S波演变成强涡旋。当通过将比边界层位移厚度薄得多的薄2-D粗糙度元素胶粘到超出线性不稳定性的关键雷诺数的位置而引入除前缘区域之外的其他接受区域时，阈值突出高度降低到60以下不存在粗糙度元素时的值的％。假设反馈环路建立在接受位置和隆起之间，通过类似于后缘噪声情况的简单反馈环路模型解释了多个离散音的频率。