The compressibility effects on the transition to turbulence in a spatially developing, compressible plane free shear layer are investigated via direct numerical simulation using a high-order discontinuous spectral element method for three different convective Mach numbers of 0.3, 0.5, and 0.7. The location of the laminar–turbulent transition zone is predicted by the analyses of vorticities, Reynolds stresses, and the turbulent dissipation rate. In the turbulence transition and self-similar turbulence regions, the effects of compressibility on the flow properties, such as the velocity autocorrelation function, integral time scale, momentum thickness, Reynolds stress, and turbulent kinetic energy budget, are investigated. The compressibility effects on the onset and length of the turbulence transition zone are studied based on the analyses of such flow properties. The mean velocity, momentum thickness, and Reynolds stress profiles compare well with published experimental data. Vorticity contours and iso-surface of the second invariant of velocity gradient tensor identify the characteristic of flow structures. The two-point correlation functions of velocity components, the one-dimensional (1D) spanwise energy spectrum, and the balance of the turbulent kinetic energy transport equation validate the domain size and resolution of the adopted grid for turbulence simulation. An increase in the convective Mach number leads to a reduction in the sizes of the largest-scale structures, resulting in a significant decrease in Reynolds stresses and turbulence production. The onset of turbulence transition and the location where the transition completes shift downstream, while the length of the transition zone increases with increasing convective Mach number.

中文翻译：

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在空间发展的平面自由剪切层中，可压缩性对湍流过渡的影响

在空间发展的可压缩平面自由剪切层中，可压缩性对湍流过渡的影响通过使用高阶不连续谱元方法的直接数值模拟对三种不同的对流马赫数 0.3、0.5 和 0.7 进行研究。层流-湍流过渡区的位置是通过涡度、雷诺应力和湍流耗散率的分析来预测的。在湍流过渡和自相似湍流区域，研究了可压缩性对流动特性的影响，如速度自相关函数、积分时间尺度、动量厚度、雷诺应力和湍流动能收支。基于对这种流动特性的分析，研究了可压缩性对湍流过渡区的开始和长度的影响。平均速度、动量厚度和雷诺应力分布与已发表的实验数据相比很好。速度梯度张量的第二不变量的涡度等值线和等值面确定了流动结构的特征。速度分量的两点相关函数、一维 (1D) 展向能谱和湍流动能输运方程的平衡验证了湍流模拟所采用网格的域大小和分辨率。对流马赫数的增加导致最大尺度结构的尺寸减小，从而导致雷诺应力和湍流产生的显着降低。