  We study two-phase stratified flow where the bottom layer is a thin laminar
liquid and the upper layer is a fully-developed gas flow. The gas flow can be
laminar or turbulent. To determine the boundary between convective and absolute
instability, we use Orr--Sommerfeld stability theory, and a combination of
linear modal analysis and ray analysis. For turbulent gas flow, and for the
density ratio r=1000, we find large regions of parameter space that produce
absolute instability. These parameter regimes involve viscosity ratios of
direct relevance to oil/gas flows. If, instead, the gas layer is laminar,
absolute instability persists for the density ratio r=1000, although the
convective/absolute stability boundary occurs at a viscosity ratio that is an
order of magnitude smaller than in the turbulent case. Two further unstable
temporal modes exist in both the laminar and the turbulent cases, one of which
can exclude absolute instability. We compare our results with an
experimentally-determined flow-regime map, and discuss the potential
application of the present method to non-linear analyses.

Fluid Dynamics