  We investigate the perturbation dynamics in a supersonic shear layer using a
combination of large-eddy simulations (LES) and linear-operator-based
input-output analysis. The flow consists of two streams-a main stream (Mach
1.23) and a bypass stream (Mach 1.0)-separated by a splitter plate of
non-negligible thickness. We employ spectral proper orthogonal decomposition to
identify the most energetic coherent structures and bispectral mode
decomposition to explore the nonlinear energy cascade within the turbulent
shear layer flow. Structures at the dominant frequency are also obtained from a
resolvent analysis of the mean flow. We observe higher gain at the dominant
frequency in resolvent analysis, indicating the dominance of Kelvin-Helmholtz
(KH) instability as the primary disturbance energy-amplification mechanism. To
focus on realizable actuator placement locations, we further conduct an
input-output analysis by restricting a state variable and spatial location of
an input and output. Various combinations of inputs and output indicate that
the splitter plate trailing surface is the most sensitive location for
introducing a perturbation. For all combinations, the KH instability plays a
key role in amplification, which reduces significantly as the input location is
moved upstream relative to the splitter plate trailing edge. Furthermore,
two-dimensional nonlinear simulations with unsteady input at the upper surface
of the splitter plate show remarkable similarities between pressure modes
obtained through dynamic mode decomposition and those predicted from linear
input-output analysis at a given frequency. This study emphasizes the strength
of linear analysis and demonstrates that predicted coherent structures remain
active in highly nonlinear turbulent flow. The insights gained from the
input-output analysis can be further leveraged to formulate practical flow
control strategies.
