Abstract
The response of a semi-infinite ocean to a slowly travelling atmospheric perturbation crossing the coast provides a simple example of the breakdown of nearly geostrophic balance induced by a boundary. We examine this response in the linear shallow-water model at small Rossby number$\varepsilon \ll 1$. Using matched asymptotics, we show that a long Kelvin wave, with$O(\varepsilon ^{-1})$length scale and$O(\varepsilon )$amplitude relative to quasi-geostrophic response, is generated as the perturbation crosses the coast. Accounting for this Kelvin wave restores the conservation of mass that is violated in the quasi-geostrophic approximation.
Highlights
This paper is motivated by fundamental aspects of quasi-geostrophic (QG) and higher-order balances in the ocean and, their accuracy in the presence of boundaries
This paper discusses a simple example of spontaneous generation of a Kelvin wave by a forced QG flow, demonstrating a fundamental limitation of the concept of balance in the presence of a boundary
The mechanism of wave generation is similar to the Lighthill radiation of acoustic waves by vortical flow: sufficiently long Kelvin waves are slow enough for their frequency to match that of the geostrophic flow, leading to a resonant response that is small, here O(ε), because of the mismatch between the spatial scales of the waves and geostrophic flow
Summary
This paper is motivated by fundamental aspects of quasi-geostrophic (QG) and higher-order balances in the ocean and, their accuracy in the presence of boundaries. Vanneste such long Kelvin waves are generated spontaneously, typically with O(ε) amplitudes, by well-balanced flows through a process analogous to Lighthill radiation. The aim of this paper is to present a straightforward example of Kelvin-wave generation by geostrophic motion in the presence of a long coast modelled as an infinite wall. We examine the response of the ocean to an atmospheric perturbation (cyclone or anticyclone) as this crosses the coast We model this process using the linear rotating shallow-water equations forced by a skew-gradient stress.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
