Open Collections

Relationships between pressure, bathymetry, and wave-height

Banff International Research Station for Mathematical Innovation and Discovery

A new method is proposed to relate the pressure at the bottom of a fluid, the shape of the bathymetry, and the surface elevation of a wave for steady flow or traveling waves. Given a measurement of any one of these physical quantities (pressure, bathymetry, or surface elevation), a numerical representation of the other two quantities is obtained via a nonlocal nonlinear equation obtained from the Euler formulation of the water-wave problem without approximation. From this new equation, a variety of different asymptotic formulas are derived. The nonlocal equation and the asymptotic formulas are compared with both numerical data and physical experiments. This is joint work with Vishal Vasan and Daniel Ferguson.

Mathematics; Fluid mechanics; Partial differential equations; Fluid dynamics

video/mp4

Author affiliation: Seattle University

2017-05-02

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/61426

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/