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Turbulent gas  laminar liquid flows
Serafim Kalliadasis
We investigate the dynamics of a thin laminar liquid film flowing under gravity
down the lower wall of an inclined channel when turbulent gas flows above the
film. The solution of the full system of equations describing the gasâ€“liquid flow faces
serious technical difficulties. However, a number of assumptions allow isolating the
gas problem and solving it independently by treating the interface as a solid wall.
This permits finding the perturbations to pressure and tangential stresses at the
interface imposed by the turbulent gas in closed form. We then analyse the liquid
film flow under the influence of these perturbations and derive a hierarchy of model
equations describing the dynamics of the interface, i.e. boundarylayer equations, a
longwave model and a weakly nonlinear model, which turns out to be the Kuramotoâ€“
Sivashinsky equation with an additional term due to the presence of the turbulent
gas. This additional term is dispersive and destabilising (for the countercurrent case;
stabilizing in the cocurrent case). We also combine the longwave approximation with
a weightedresidual technique to obtain an integralboundarylayer approximation
that is valid for moderately large values of the Reynolds number. This model is
then used for a systematic investigation of the flooding phenomenon observed in
various experiments: as the gas flow rate is increased, the initially downwardfalling
film starts to travel upwards while just before the wave reversal the amplitude of the
waves grows rapidly. We confirm the existence of largeamplitude stationary waves by
computing periodic travelling waves for the integralboundarylayer approximation
and we corroborate our travellingwave results by timedependent computations.

