2D and 3D Modes in Supersonic Mach number Open Cavity Flows*

The coupled resonant oscillations in shallow open cavity flows at supersonic Mach numbers (1.4-3) are investigated for a fixed L/D ratio (6), depth-based Reynolds number (10,000), and incoming boundary layer thickness. By combining local spatial stability and global resolvents, it is demonstrated that increasing the freestream Mach number in this parameter range could lead to a destabilization of higher order 2D modes due to a shift in the convective Mach number of the underlying instabilities from subsonic to supersonic within the cavity. The mode shapes reveal that when the convective Mach number is supersonic, these instabilities are not only associated with growth rates that are comparable to those at subsonic convective Mach numbers, they also support waves that reflect back and forth between the shear layer and the cavity floor, thus providing a mechanism for instability that is not typically found at subsonic freestream Mach numbers. Furthermore, by varying the spanwise wavenumber, it is observed that an increase in Mach number in this range renders the cavity more three-dimensional due to reduced differences between the gain of the 2D and 3D modes. The results of this study are especially pertinent to the design of flameholders that operate in the supersonic regime.