A Simple Model for Capillary Waves Propagating over Static Curved Surfaces

The distortion of propagating pure capillary waves due to curved free-surfaces, such as menisci, is an underexplored area of study. Previous works on fluid waves on curved free-surfaces focused on the interactions of gravity-capillary waves with menisci in edge constraint problems, suddenly accelerated surfaces, and the formation of parasitic capillary waves. Here, inspired by studies on Rayleigh waves propagating over curved surfaces, we present a simple inviscid model to understand how the propagation of small amplitude, high frequency capillary waves are affected by an underlying static, curved surface. Additionally, we discuss future avenues to extend our analysis to include viscous effects and relax our high frequency assumptions.