What Fraction of a Kelvin Wave Incident on a Narrow Strait Is Transmitted?

Abstract

Parameters governing the fraction of a Kelvin wave transmitted through a narrow gap or channel include time dependence, nonlinearity, friction, and strait geometry, yet only limited regions of this parameter space have been explored. Linear inviscid models (which neglect advective and frictional terms in the momentum equations) predict that 100% of the volume flux of a low-frequency Kelvin wave or steady boundary current incident on a narrow strait is transmitted, even when the strait width becomes infinitesimally small. Here the nonlinear, inviscid, flat bottom problem is considered, and it is shown that, provided the geometry varies slowly, the quasi-steady solution can be found in the rotating-hydraulics literature. In the narrow channel limit the fraction transmitted can be approximated by a simple prediction based on nonrotating hydraulics. Unless an incoming Kelvin wave has a large amplitude in comparison with the background layer depth, the strait width must be considerably smaller than the deformation radius before it limits the volume flux passing through. Results also show that a Kelvin wave of given volume flux will squeeze through a narrower gap if it is pushed rather than pulled.