  Roll-wave trains constitutes a well-known two-phase flow regime in pipes.
There exists a one-parameter family of steady roll-wave train solutions,
provided the flow conditions are within the roll-wave range. This means that
wave train solutions can be constructed from out of a wide range of
wavelengths. That band of wavelengths which will be observed in nature is
however fairly narrow. The wavelength distribution is believed to be related to
wave train stability and the flow disturbances.
  Steady roll-wave train solutions are in this article subjected to a linear
stability analysis. Comparisons are made with predictions from direct numerical
Roe scheme simulations. Good agreement is observed; after an initial stage of
wave coalescence, simulated wavelengths are distributed among the shorter of
those wavelengths which are predicted linearly stable. Also the observed
disturbance frequency and rate of decay agrees with the analysis predictions.
Finally, the stability of pressure driven gas-liquid trains is compared to that
of gravity driven free surface trains.
