During my PhD work I investigated the junction between a closed conduit and an open channel, and therefore addressed presumably similar concerns as yours. I looked at the influlence of some boundary conditions and hydrodynamic factors on flow mode in pipe.
Though I cannot readily answer your question, maybe will you find elements or useful references in two documents I wrote : my PhD (sorry it's in French) "Interactions en crue entre drainage souterrain et assainissement agricole" and a paper in Journal of Hydraulic Engineering "Experimental Study of a Right-Angled End Junction between a Pipe and an Open Channel".
Please send additional elements of context that may improve my answer if these first elements seemed relevant to you...
Right now i am working on two-phase (air-water) pipe flow. I read number of the papers on two-phase flow particularly on slug flow but still it is not clear that the K-H instability is responsible for onset of slug flow. So i am wondering about the physics behind the formation of slug flow.
i'm working on the same topic, developing a model to predict slug flow with consideration of the entrainment in CMFD. The experiments at our department have shown, that both KH-instability in combination with Bernoulli effect but most of all wave coalescence are playing an important role for the onset of slug flow, where the onset of perturbations from stratified flow seems to be an fully stochastical phenomenon. Ones the coalesced wave is high enough surface perturbations on the wave top, due to the very high local gas velocity caused by the narrowed cross section, are responsible for the "blocking" of the hole cross section by the liquid. After that, the slug is accelerated nearly to gas velocity, while it is growing entraining gas and liquid at the slug front. There is a lot work done in this field at our chair, maybe i can give you some related literature if you are interested.
If you have some good literature about developing the slug flow due to influence of k-h instability and Bernoulli effect then please send it to me. Because this will help me to understand the physics behind the onset of slug flow.