Numerical analysis of acoustic radiation vortical modes in a spatially evolving supersonic plane shear layer

Disturbance modes and flow structures are numericallyanalyzed for a two-dimensional spatially evolving supersonic plane freeshear layer at Mc = 1.2. The compressible disturbance Navier-Stokesequations are solved by using a modified MacCormack scheme, which is athird-order method in both temporal and spatial accuracies. Three primaryharmonic-wave disturbances with different frequencies are superimposed uponthe mean transverse velocities at inflow sections, and then their nonlineardevelopments are investigated by using the direct numerical simulation (DNS)method. Moreover, a spatial linear stability theory is also introduced, and itis shown that the induced disturbance waves obtained by the DNS methodare ofacoustic radiation vortical modes. The results from analyses of disturbanceparameters and eigenfunctions reveal that the acoustic radiation vorticalmode is an outer mode consisting of fast and slow modes, radiating in thesupersonic disturbance convective Mach number side in the shear layer, witha series of expansion and compression fans. Single-frequency forcingdisturbance can produce a multi-mode mixed disturbance wave without phasedifference, while the slow mode is dominant in the shear layer for a naturaldisturbance.