  We present an analysis of the linear stability characteristics of
shock-containing jets. The flow is linearised around a spatially periodic mean,
which acts as a surrogate for a mean flow with a shock-cell structure, leading
to a set of partial differential equations with periodic coefficients in space.
Disturbances are written using the Floquet ansatz and Fourier modes in the
streamwise direction, leading to an eigenvalue problem for the Floquet
exponent. The characteristics of the solution are directly compared to the
locally parallel case, and some of the features are similar. The inclusion of
periodicity induces minor changes in the growth rate and phase velocity of the
relevant modes for small shock amplitudes. On the other hand, the
eigenfunctions are now subject to modulation related to the periodicity of the
flow. Analysis of the spatio-temporal growth rates led to the identification of
a saddle point between the Kelvin-Helmholtz mode and the guided jet mode,
characterising an absolute instability mechanism. Frequencies and mode shapes
related to the saddle points for two conditions (associated with axisymmetric
and helical modes) are compared with screech frequencies and the most energetic
coherent structures of screeching jets, resulting in a good agreement for both.
The analysis shows that a periodic shock-cell structure has an impulse response
that grows upstream, leading to oscillator behaviour. The results suggest that
screech can occur in the absence of a nozzle, and that the upstream reflection
condition is not essential for screech frequency selection. Connections to
previous models are also discussed.
