  We report on ab initio simulation of fluid interface deformations induced
either by acoustic or optical radiation pressure. This is done by solving
simultaneously the scalar wave propagation equation and the two-phase flow
equations using the boundary element method. Using dimensional analysis, we
show that interface deformation morphogenesis is universal, i.e. depends on the
same dimensionless parameters in acoustics and electromagnetics. We numerically
investigate a few selected phenomena -- in particular the shape of large
deformations, the slenderness transition and its hysteresis -- and compare with
existing and novel experimental observations. Qualitative agreement between the
numerical simulations and experiments is found when the mutual interaction
between wave propagation and wave-induced deformations is taken into account.
Our results demonstrate the leading role of the radiation pressure in
morphogenesis of fluid interface deformations and the importance of the
propagation-deformation interplay .
