  In this paper, we develop an analytical model to investigate the generation
of instability waves triggered by the upstream acoustic forcing near the nozzle
lip of a supersonic jet. This represents an important stage, i.e. the jet
receptivity, of the screech feedback loop. The upstream acoustic forcing,
resulting from the shock-instability interaction, reaches the nozzle lip and
excites new shear-layer instability waves. To obtain the newly-excited
instability wave, we first determine the scattered sound field due to the
upstream forcing using the Wiener-Hopf technique, with the kernel function
factored using asymptotic expansions and overlapping approximations.
Subsequently, the unsteady Kutta condition is imposed at the nozzle lip,
enabling the derivation of the dispersion relation for the newly-excited
instability wave. A linear transfer function between the upstream forcing and
the newly-excited instability wave is obtained. We calculate the amplitude and
phase delay in this receptivity process and examine their variations against
the frequency. The phase delay enables us to re-evaluate the phase condition
for jet screech and propose a new frequency prediction model. The new model
shows improved agreement between the predicted screech frequencies and the
experimental data compared to classical models. It is hoped that this model may
help in developing a full screech model.
