Interfacial instability in turbulent ow over a liquid lm in a channel

We revisit the stability of a deformable interface that separates a fully-developed turbulent gas ow from a thin layer of laminar liquid. Although this problem has received considerable attention previously, a model that requires no tting parameters and that uses a base-state prole that has been validated against experiments is, as yet, unavailable. Furthermore, the signicance of wave-induced perturbations in turbulent stresses remains unclear. To address these outstanding issues, we investigate this problem and introduce a turbulent base-state velocity that requires specication of a ow rate or a pressure drop only; no adjustable parameters are necessary. This base state is validated extensively against available experimental data as well as the results of direct numerical simulations. In addition, the eect of perturbations in the turbulent stress distributions is investigated, and demonstrated to be small for cases wherein the liquid layer is thin. The detailed modelling of the liquid layer also elicits two unstable modes, `interfacial ' and `internal', with the former being the more dominant of the two. We show that it is possible for interfacial roughness to reduce the growth rate of the interfacial mode in relation to that of the internal one, promoting the latter, to the status of most dangerous mode. Additionally, we introduce an approximate measure to distinguish between `slow ' and `fast ' waves, the latter being the case for `critical-layer'-induced instabilities; we demonstrat