Scaling of amplitude and pitch of surface ripples after welding solidification

The average amplitude and pitch of surface ripples after solidification are exploratorily interpreted from scale analysis and numerical computation of transport variables and free surface deformation in a molten pool. Rippling influences welding, additively manufacturing and nano-technologies. By accounting for solid speed and oscillation of fluid velocity, the results find that amplitude is proportional to the difference in surface pressures and mechanical energy losses between edge and centre regions. Pitch is determined by the product of solid speed with timescale for surface displacement. The ratios between solid speed and liquid velocity near the central and pool edge regions, respectively, determine amplitude and pitch. Rather than pitch, oscillating flow is insensitive to amplitude. Transport fields solved by COMSOL code confirm scaled results.