Flow structure underneath the large amplitude waves of a vertically falling film

Numerical solutions of the two-dimensional Navier-Stokes equations for vertically falling films show that when the wave amplitude exceeds a certain magnitude, two hyperbolic points on the wall and an elliptic point in the film are generated below the minimum of the wave and travel at the wave velocity. The shear stress along the wall between the hyperbolic points becomes negative and the instantaneous flow field in the film shows roll formation with flow reversal near the wall region. As the wave amplitude increases further, these rolls expand to the free surface dividing the film into regions of up and down flows. For high Kapitza number fluids such as water, multiple regions of up-flow and negative wall shear stress exist with their width oscillating in time. The flow field is interpreted in both stationary and moving frames of reference and in explaining transport enhancements at the wall and free surface. (C) 2008 American Institute of Chemical Engineers.