Pressure transfer functions for interfacial fluid problems

TL;DR

This paper derives pressure transfer functions for interfacial fluid problems considering vorticity, stratification, and internal waves, extending classical results to more complex flow conditions.

Contribution

It provides a consistent derivation of pressure transfer functions incorporating vorticity, stratification, and internal waves, extending classical zero-vorticity formulas.

Findings

Derived pressure transfer functions with vorticity effects

Extended formulas to stratified and internal wave scenarios

Results agree with classical formulas in zero-vorticity limit

Abstract

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.