Nonlinear interactions of the global instabilities in hypersonic laminar flow over a double cone

Hypersonic laminar flow over a canonical 25‒55{degree sign} double cone is studied using computational fluid dynamics, bispectrum analysis, and dynamic mode decomposition (DMD) with a freestream Mach number of 11.5 and unit Reynolds number of 1.6 × 105 m−1. The present study focuses on the evolution and nonlinear behavior of perturbation modes in the flow. The presence of the perturbation modes is first described in detail through the results of direct numerical simulation (DNS). The results of high-order spectrum analysis (bispectrum) then reveal complex nonlinear interactions in the flow. By examining the evolution of such interactions, the frequency broadening phenomenon of the fully saturated flow is explained, and the unsteady dynamics of the fully saturated flow are recognized to be caused by the nonlinear saturation of linear instability in the flow. This causality is further confirmed by the DMD results of the Stanton number near the reattachment region. The origins and dynamics of unsteady saturated flow in the hypersonic laminar flow are therefore demonstrated.