Experimental study of shear layer instability below a free surface

Abstract

Relaxation of a laminar boundary layer at a free surface is an inviscidly unstable process and can lead to millimeter-scale surface waves, influencing interfacial processes. Due to the small time- and length-scales involved, previous experimental studies have been limited to visual observations and point-wise measurements of the surface profile to determine instability onset and frequency. However, effects of viscosity, surface tension, and non-linearity of the wave profile have not been systematically studied. In fact, no data have been reported on the velocity fields associated with this instability. In the present study, planar laser induced fluorescence and particle image velocimetry provide surface profiles coupled with liquid phase velocity fields for this instability in a time resolved manner. Wave steepness (ak, with a the amplitude and k the wave number) and Reynolds andWeber numbers based on momentum thickness range from 0 to 1.2, 143 to 177, and 4.79 to 6.61, respectively. Large datasets are analyzed to gain statistical information on the surface behavior. Discrete vortices are resolved, showing that the shear layer becomes unstable and rolls up above a Reynolds number of 140. The detection onset and steepness of the subsequent surface deformation by the vortices depend upon the Weber number. Non-linear behavior such as vortex motion and wave profile asymmetry are observed at steepness larger than 0.5.