The Rossiter modes of an open cavity were studied using bi-global linear analysis, local instability analysis and nonlinear numerical simulations. Rossiter modes are normally seen only for short cavities; hence, in the study, the length over depth ratio was two. We focus on the critical region; hence, the Reynolds numbers based on cavity depth were close to 1000. We investigated the effect of the ratio boundary layer thickness to cavity depth, a parameter often overlooked in the literature. Increasing this ratio is destabilizing and increases the number of unstable Rossiter modes. Local instability analysis revealed that the hierarchy of unstable modes was governed by the mixing in the cavity opening. The effect of Mach number was also studied for thin and thick boundary layers. Compressibility had a very destabilizing effect at low Mach numbers. Analysis of the Rossiter mode eigenfunctions indicated that the acoustic feedback scaled to \(\mathrm{Ma}^3\) and explained the strong destabilizing effect of compressibility at low Mach numbers. At moderate Mach numbers, the instability either saturated with Mach number or had an irregular dependence on it. This was associated with resonances between Rossiter modes and acoustic cavity modes. The analysis explained why this irregular dependence occurred only for higher-order Rossiter modes. In this parameter region, three-dimensional modes are either stable or marginally unstable. Two-dimensional simulations were performed to evaluate how much of the nonlinear regime could be captured by the linear stability results. The instability was triggered by the \(10^{-13}\) flow solver noise floor. The simulations initially agreed with linear theory and later became nonlinearly saturated. The simulations showed that, as the flow becomes more unstable, an increasingly more complex final stage is reached. Yet, the spectra present distinct tones that are not far from linear predictions, with the thin boundary layer cases being closer to empirical predictions. The final stage, in general, was dominated by first Rossiter mode, even though the second one was the most unstable linearly. It seems this may be associated with nonlinear boundary layer thickening, which favors lower frequency in the mixing layer, or vortex pairing of the second Rossiter mode. The spectra in the final stages are well described by the mode R1 and a cascade of nonlinearly generated harmonics, with little reminiscence of the linear instability.

使用双全局线性分析，局部不稳定性分析和非线性数值模拟研究了开放腔的Rossiter模。通常仅在短腔中才能看到Rossiter模式。因此，在研究中，长度与深度之比为2。我们专注于关键区域。因此，基于腔深度的雷诺数接近于1000。我们研究了边界层厚度与腔深度之比的影响，这是文献中经常忽略的参数。增大此比率会破坏稳定性，并增加不稳定的Rossiter模式的数量。局部不稳定性分析表明，不稳定模式的层次由空腔开口中的混合控制。还研究了马赫数对薄边界层和厚边界层的影响。在低马赫数下，可压缩性具有非常不稳定的作用。\（\ mathrm {Ma} ^ 3 \）并解释了在低马赫数下可压缩性的强大去稳定作用。在中等马赫数下，不稳定性会随马赫数饱和或对其不规则依赖。这与Rossiter模和声腔模之间的共振有关。分析解释了为什么这种不规则依赖性仅在高阶Rossiter模中发生。在此参数区域中，三维模式是稳定的或略微不稳定的。进行了二维仿真，以评估线性稳定性结果可以捕获多少非线性状态。不稳定性是由\（10 ^ {-13} \）触发的流量求解器的本底噪声。这些模拟最初与线性理论相符，后来变成非线性饱和。仿真表明，随着流量变得更加不稳定，最终阶段将变得越来越复杂。然而，频谱呈现出与线性预测相距不远的独特色调，而薄边界层的情况更接近于经验预测。通常，最后一个阶段由第一个Rossiter模式控制，即使第二个线性上最不稳定。看来这可能与非线性边界层增厚有关，非线性边界层增厚倾向于在混合层中使用较低的频率，或者是第二Rossiter模式的涡旋配对。最终阶段的光谱通过模式R1和一系列非线性生成的谐波很好地描述了，很少回想起线性不稳定性。