Linear and nonlinear evolution of disturbances in an axisymmetric, supersonic, low Reynolds number jet is studied using parabolized stability equations approach. Both axisymmetric and helical modes are considered and nonparallel effect is found to increase the disturbance growth rate, although there is very little effect on the wavenumber. Nonlinear interaction of the helical modes, which are the dominant instability modes of the jet, results in disturbance saturation, spectrum filling and large mean flow distortions. Similar to that for the supersonic boundary layer flow (Chang, C.-L., Malik, M.R., Oblique-mode breakdown and secondary instability in supersonic boundary layers. J. Fluid Mech. 273(1994) 323-359), interaction of the helical modes induces streamwise vortices which cause significant mean flow distortion and growth of other harmonics. The computed evolution of disturbances is in reasonably good agreement with the experimental data of Morrison and McLaughlin (Morrison. G.L.. McLaughlin, D.K., Instability process in low Reynolds number supersonic jets. AIAA J. 18(7) (1980) 793 800). The present marching scheme is able to compute evolution of supersonic disturbances without any numerical reflections and the induced far-field pressure disturbance is found to be almost in phase with the acoustic wave at ambient conditions.
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机译：使用抛物稳定方程方法研究了轴对称，超音速，低雷诺数射流中扰动的线性和非线性演化。尽管对波数影响很小，但同时考虑了轴对称模式和螺旋模式，并且发现非平行效应会增加扰动增长率。螺旋模式的非线性相互作用是喷射的主要不稳定模式，导致扰动饱和，频谱填充和较大的平均流量畸变。类似于超音速边界层流动（Chang，C.-L.，Malik，MR，超声速边界层中的斜模破坏和次要不稳定性。J.流体力学273（1994）323-359），相互作用螺旋模式会引起沿流的涡流，从而引起明显的平均流畸变和其他谐波的增长。计算得出的扰动演化与Morrison和McLaughlin的实验数据相当吻合（Morrison。G.L. McLaughlin，D.K.，低雷诺数超音速喷气机的失稳过程，AIAA J. 18（7）（1980）793 800）。当前的行进方案能够在没有任何数值反射的情况下计算超音速扰动的演变，并且在环境条件下，感应的远场压力扰动几乎与声波同相。
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