Spanwise effects on instabilities of compressible flow over a long rectangular cavity

The stability properties of two-dimensional (2D) and three-dimensional (3D) compressible flows over a rectangular cavity with length-to-depth ratio of L/ D= 6 are analyzed at a free-stream Mach number of M_∞= 0.6 and depth-based Reynolds number of Re_D= 502. In this study, we closely examine the influence of three-dimensionality on the wake mode that has been reported to exhibit high-amplitude fluctuations from the formation and ejection of large-scale spanwise vortices. Direct numerical simulation (DNS) and bi-global stability analysis are utilized to study the stability characteristics of the wake mode. Using the bi-global stability analysis with the time-averaged flow as the base state, we capture the global stability properties of the wake mode at a spanwise wavenumber of β= 0. To uncover spanwise effects on the 2D wake mode, 3D DNS are performed with cavity width-to-depth ratio of W/ D= 1 and 2. We find that the 2D wake mode is not present in the 3D cavity flow with W/ D= 2 , in which spanwise structures are observed near the rear region of the cavity. These 3D instabilities are further investigated via bi-global stability analysis for spanwise wavelengths of λ/ D= 0.5 - 2.0 to reveal the eigenspectra of the 3D eigenmodes. Based on the findings of 2D and 3D global stability analysis, we conclude that the absence of the wake mode in 3D rectangular cavity flows is due to the release of kinetic energy from the spanwise vortices to the streamwise vortical structures that develops from the spanwise instabilities.