  The stability characteristics of compressible spanwise-periodic open-cavity
flows are investigated with direct numerical simulation and biglobal stability
analysis for rectangular cavities with aspect ratios of $L/D=2$ and 6. This
study examines the behavior of instabilities with respect to stable/unstable
steady states in the laminar regimes for subsonic and transonic conditions
where compressibility plays an important role. It is observed that an increase
in Mach number destabilizes the flow in the subsonic regime and stabilizes the
flow in the transonic regime. Biglobal stability analysis is conducted to
extract 2D and 3D eigenmodes for prescribed spanwise wavelengths about the 2D
steady state. The properties of 2D eigenmodes agree well with those observed in
the 2D nonlinear simulations. In the analysis of 3D eigenmodes, it is found
that an increase of Mach number stabilizes dominant 3D eigenmodes. For a short
cavity with $L/D=2$, the 3D eigenmodes primarily stem from centrifugal
instabilities. For a long cavity with $L/D=6$, other types of eigenmodes appear
whose structures extend from the aft-region to the mid-region of the cavity. A
selected number of 3D DNS are performed at $M_\infty=0.6$. For $L/D=2$, the
properties of 3D structures present in the 3D nonlinear flow correspond closely
to those obtained from linear stability analysis. However, for $L/D=6$, the 3D
eigenmodes cannot be clearly observed in the 3D DNS, due to the strong
nonlinearity that develops over the length of the cavity. In addition, it is
noted that three-dimensionality in the flow helps alleviate violent
oscillations for the long cavity. The analysis performed in this paper can
provide valuable insights for designing effective flow control strategies to
suppress undesirable aerodynamic and pressure fluctuations in compressible
open-cavity flows.
