2015/10/08 by Vera Mikyoung Hur, Hur, Vera Mikyoung, Michael Livesay +2
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Coastal and Marine Dynamics #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Mathematical Physics (math-ph) #Ocean Waves and Remote Sensing #Oceanographic and Atmospheric Processes #math-ph #math.AP #math.MP #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1510.02396
arxiv created 2015/10/08 · openalex publication_date 2015/10/08 · arxiv updated 2015/10/09 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
We propose higher-order approximation formulae recovering the surface elevation from the pressure at the bed and the background shear flow for small-amplitude Stokes and solitary water waves. They offer improvements over the pressure transfer function and the hydrostatic approximation. The formulae compare reasonably well with asymptotic approximations of the exact relation between the pressure at the bed and the surface wave in the zero vorticity case, but they incorporate the effects of vorticity through solutions of the Rayleigh equation. Several examples are discussed.