Hydrodynamic instabilities and coherent structures. Progress report, January 1--December 31, 1995

Study was continued on the three-dimensional waves on films flowing down solid surfaces which are governed by an evolution equation derived earlier. They have analytically found 2-D travelling wave solutions of their equation. In accordance with II-1 of the Summary, they have refined their multi-parametric perturbation approach in two directions. First, they obtain, along with the evolution equation and explicit expressions for velocities and pressures in terms of film thickness, the conditions of both local (in time) and global validity of the theory. Second, the procedure was made more algorithmic, and they can claim that it now yields the most general of the possible leading-order evolution equations. They have completed work planned on the derivation of the next-order correction to their Benney-type equation for a film falling down a vertical cylinder. They have obtained the critical conditions for onset of large-scale instability in generalized Kolmogorov flows. A detailed account of the work on large-amplitude waves in core-annular flows was published in the Journal Of Fluid Mechanics. Plans for next year are discussed