Nonlinear dynamics of sound production by a mixing layer: an investigation using Lyapunov covariant vectors*

Current design process of noise control is empirical and depends on expensive rig test data. We aim to use eddy resolving simulation along with Lyapunov analysis to understand the nonlinearity in sound source compared with linear wavepackets and provide physical insights into chevron design. In this research, a mixing layer with Re_δ^*=300 is designed to produce the basic ingredients of jet mixing noise. 152 largest Lyapunov exponents are obtained and neutral modes are reached around the 100^th Lyapunov exponent.  Vorticity and pressure components of the covariant Lyapunov vectors are investigated and compared with Spectral POD (SPOD) modes (linear wavepackets). It is found that the similarity between covariant Lyapunov vectors and SPOD modes exist at the early stage of shear layer development. This indicates that the nonlinearity becomes more important in the late stage, which might be linked with the missing intermittency dynamics in wavepackets model. This database will be used for computation of sensitivity information of serration change and far-field sound to near-field source using both tangent and adjoint method in the future.