Interplay of viscosity and surface tension for ripple formation by laser melting

A model for ripple formation on liquid surfaces exposed to an external laser or particle beam and a variable ground is developed. The incident hereby mechanically coupled the surface due roughness. Starting from Navier Stokes equation equations velocity potential height are derived in shallow-water approximation with special attention viscosity. resulting obey conservation laws volume momentum where characteristic potentials gravitation tension identified analogously conservative forces. approximate solutions discussed context of materials processing involving melting by beam. Linear stability analysis provides damped wave modified interplay between beam, viscosity, tension. limit small viscosity leads gravitational high capillary waves. wavelengths order ripples occurring welding experiments hinting involvement hydrodynamic processes their origin. By discussing response system periodic excitations help Floquet multipliers, we show that could be triggered periodically modulated e.g. appropriate repetition rates weak nonlinear ranges hexagonal stripe structures can appear. orientation shown dependent angle minimal reported. Numerical simulations confirm findings allow describe influence grounds.