Nonlinear transient disturbance growth analysis for the compressible external flow and application to a flow around circular cylinder

The property of nonlinear optimal perturbation (NLOP) analysis for the flow around the circular cylinder was investigated with a comparison with the linear optimal perturbation analysis (LOP). Our analysis revealed that NLOP is highly dependent on the initial disturbance norm and highlighted the limitation of linear prediction in triggering instability in the flow field. This NLOP shows an asymmetric and deformed vortex structure on the cylinder wall, with the angle of the maximum wall vorticity shifting in relation to the initial disturbance norm. We also observed that the circulation and disturbance vorticity at the shear layer in boundary layer efficiently contributed to larger disturbance growth of the separation vortex behind the cylinder compared with the LOP. • NLOP method was successfully applied to flow around a circular cylinder. • Effect of initial disturbance and evaluation time on NLOP mode was clarified. • How the time evolution of NLOP disturbance deviates from LOP was elucidated. • LOP generates strong disturbance around the separation point on the surface. • NLOP concentrated in boundary layer, moves separation point forwards.