Numerical investigation of wave steepening and shock coalescence near a cold Mach 3 jet^a)

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.