  The resolvent formulation of McKeon & Sharma (2010) is applied to supersonic
turbulent boundary layers to study the validity of Morkovin's hypothesis, which
postulates that high-speed turbulence structures in zero pressure-gradient
turbulent boundary layers remain largely the same as its incompressible
counterpart. Supersonic zero-pressure-gradient turbulent boundary layers with
adiabatic wall boundary conditions at Mach numbers ranging from 2 to 4 are
considered. Resolvent analysis highlights two distinct regions of the
supersonic turbulent boundary layer in the wave parameter space: the relatively
supersonic region and the relatively subsonic region. In the relatively
supersonic region, where the flow is supersonic relative to the freestream,
resolvent modes display structures consistent with Mach wave radiation that are
absent in the incompressible regime. In the relatively subsonic region, we show
that the low-rank approximation of the resolvent operator is an effective
approximation of the full system and that the response modes predicted by the
model exhibit universal and geometrically self-similar behaviour via a
transformation given by the semi-local scaling. Moreover, with the semi-local
scaling, we show that the resolvent modes follow the same scaling law as their
incompressible counterparts in this region, which has implications for
modelling and the prediction of turbulent high-speed wall-bounded flows. We
also show that the thermodynamic variables exhibit similar mode shapes to the
streamwise velocity modes, supporting the strong Reynolds analogy. Finally, we
demonstrate that the principal resolvent modes can be used to capture the
energy distribution between momentum and thermodynamic fluctuations.
