Abstract
Flows of incompressible inviscid heavy fluids with free or rigid boundary surfaces are considered. For slender streams of fluid, the flow and the free boundaries are represented by a number of different asymptotic expansions in powers of the slenderness ratio. There are three kinds of outer expansions representing respectively jets, which have two free boundaries, wall flows, which have one free and one rigid boundary, and channel flows, which have two rigid boundaries. The flow at the junction of two or more outer flows is represented by an inner expansion. Previously we constructed the three outer expansions and the inner expansion at the junction of a wall flow and a jet (Keller & Geer 1973). Now we construct the inner expansions at the junctions of a channel flow and a jet, a channel flow and a wall flow, and a jet and the two wall flows into which it splits upon hitting a wall. We also match each inner expansion to the adjacent outer expansions. These seven expansions can be combined to solve many problems involving flows of slender streams.
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