Pressure transfer functions for interfacial fluid problems

We make a consistent derivation, from the governing equations, of the pressure transfer function in the small-amplitude Stokes wave regime and the hydrostatic approximation in the small-amplitude solitary water wave regime, in the presence of a background shear flow. The results agree with the well-known formulae in the zero vorticity case,but they incorporate the effects of vorticity through solutions to the Rayleigh equation. We extend the results to permit continuous density stratification and to internal waves between two constant-density fluids. Several examples are discussed.