  A combined analytical and numerical study is conducted to investigate the
asymmetric cap-shock non-uniform Mach Reflection (csMR) phenomenon outside of
an over-expanded supersonic jet. Prior analytical works have only considered
the wedge-induced steady symmetric and asymmetric Mach reflection (MR)
configurations, as well as symmetric MR in an open jet. However, there is
another structure occurring in nozzle flow fields known as a non-uniformity
induced cap-shock pattern. We derive a new analytical model to predict the wave
structure of the asymmetric csMR in the absence of internal shocks by extending
on a prior symmetric Mach reflection model. Different from the wedge flow case,
flow non-uniformity is incorporated by assuming different upstream Mach numbers
in both upper and lower domains, where the asymmetry is predicted through
averaged flowfields and slipstream inclination angles. The numerical approach
utilises an Euler solver for comparisons to the developed theory. It is found
that the model adequately predicts the shock structure obtained from numerical
simulations, and can be utilised for various sets of parameters to capture the
overall direct Mach reflection o[DiMR+DiMR] configuration. The von Neumann
criterion is also well captured by the new analytic model, along with the Mach
stem profile and shock curvatures. Based on the analytical and numerical
observations, a hypothesis is also made regarding the stability of MR
structures within an over-expanded jet.
