Abstract

For mid-latitude Rossby waves (RWs) in the atmosphere, the expression for the energy flux for use in a model diagnosis, and without relying on a Fourier analysis or a ray theory, has previously been derived using quasi-geostrophic equations and is singular at the equator. By investigating the analytical solution of both equatorial and mid-latitude waves, the authors derive an exact universal expression for the energy flux which is able to indicate the direction of the group velocity at all latitudes for linear shallow water waves. This is achieved by introducing a streamfunction as given by the inversion equation of Ertel’s potential vorticity, a novel aspect for considering the energy flux. For ease of diagnosis from a model, an approximate version of the universal expression is explored and illustrated for a forced/dissipative equatorial basin mode simulated by a single-layer oceanic model that includes both mid-latitude RWs and equatorial waves. Equatorial Kelvin Waves (KWs) propagate eastward along the equator, are partially redirected poleward as coastal KWs at the eastern boundary of the basin, and then shed mid-latitude RWs that propagate westward into the basin interior. The connection of the equatorial and coastal waveguides has been successfully illustrated by the approximate expression of the group-velocity-based energy flux of the present study. This will allow for tropical-extratropical interactions in oceanic and atmospheric model outputs to be diagnosed in terms of an energy cycle in a future study.

Highlights

  • A feature of many phenomena in the equatorial oceans is the role played by equatorial Kelvin waves (KWs), examples being El Niño Southern Oscillation (ENSO; Philander 1989) and the so-called Atlantic Niño (Merle 1980)

  • KWs propagate along the equator and are partially redirected into coastal KWs at the eastern boundary, where they can influence off-equatorial latitudes (e.g., Lübbecke et al 2010) as well as excite extratropical Rossby waves (RWs) that subsequently propagate into the ocean interior (McPhaden and Ripa 1990; Isachsen et al 2007)

  • After reflection at the western boundary, it takes only a quarter of a cycle (i.e., T∗/4) for equatorial KWs to travel eastward to the eastern boundary of the model domain, where some disturbances are deflected poleward along the eastern boundary to be the source of mid-latitude RWs which propagate westward (Fig. 5b)

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Summary

Introduction

A feature of many phenomena in the equatorial oceans is the role played by equatorial Kelvin waves (KWs), examples being El Niño Southern Oscillation (ENSO; Philander 1989) and the so-called Atlantic Niño (Merle 1980). By investigating the analytical solution of equatorial waves, we derive an exact universal expression for the rotational flux which, after being added to V∗p∗, is able to indicate the direction of the group velocity for linear waves at all latitudes.

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