Wave evolution on a falling film

Since the pioneering experiment by the father-son team of the Kapitza family during their house arrest in the late forties (Kapitza & Kapitza 1949), wave evolution on a falling film has intrigued many researchers. One of its main attractions is its simplicity-it is an open-flow hydrodynamic instability that occurs at very low flow rates. It can hence be studied with the simplest experimental apparatus, an obviously important factor for the Kapitzas. Yet, it yields a rich spectrum of fascinating wave dynamics, including a very unique and experimentally well-characterized sequence of nonlinear secondary transitions that begins with a selected monochromatic disturbance and leads eventually to nonstationary and broad-banded (in both frequency and wave number) "turbulent" wave dynamics. (Turbu­ lence here is used interchangeably with irregular spatio-temporal fluc­ tuations.) While this transition to "interfacial turbulence" or "spatio­ temporal chaos" seems to be quite analogous to other classical instabilities at first glance, there are subtle but important differences that have recently come to light. The pertinent nonlinear mechanisms behind these secondary transitions are the focus of the present review. We shall be mostly concerned with transitions on a free-falling vertical film. Wave dynamics on an inclined plane is quite analogous to the vertical limit and most experiments and theories have focused on the latter. For the vertical film, the problem is defined by two independent dimensionless parameters and we prefer the Russian convention of using the Reynolds