Wave steepening and shock coalescence due to nonlinear propagation effects are investigated for a cold Mach 3 jet. The jet flow and near pressure fields are computed using large-eddy simulation. The near acoustic field is propagated to the far field by solving the linearized or the weakly nonlinear Euler equations. Near the angle of peak levels, the skewness factors of the pressure fluctuations for linear and nonlinear propagations display positive values that are almost identical. Thus, the positive asymmetry of the fluctuations originates during the wave generation process and is not due to nonlinear propagation effects. Compressions in the signals are much steeper for a nonlinear than for a linear propagation, highlighting the crucial role of nonlinear distortions in the formation of steepened waves. The power transfers due to nonlinear propagation are examined for specific frequencies by considering the spatial distribution of the Morfey–Howell indicator in the near and far acoustic fields. They are in good agreement with the direct measurements performed by comparing the spectra for nonlinear and linear propagations. This shows the suitability of the Morfey–Howell indicator to characterize nonlinear distortions for supersonic jets.

中文翻译：

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马赫3冷射流附近波增陡和激波合并的数值研究

对于冷的马赫3射流，研究了由于非线性传播效应引起的波变陡和激波合并。使用大涡模拟计算射流和近压力场。通过求解线性化或弱非线性欧拉方程，将近声场传播到远场。在峰值水平的角度附近，线性和非线性传播的压力波动偏度因子显示几乎相同的正值。因此，波动的正不对称性是在波产生过程中产生的，而不是由于非线性传播效应引起的。对于非线性而言，信号中的压缩要比线性传播中的更为陡峭，这突出了非线性失真在陡峭波的形成中的关键作用。通过考虑近距离和远距离声场中Morfey-Howell指示器的空间分布，可以检查特定频率下非线性传播引起的功率传递。它们与通过比较非线性和线性传播的光谱进行的直接测量非常吻合。这表明Morfey-Howell指示器适用于表征超音速喷射的非线性畸变。