| Summary: | The propagation of planetary, or Rossby, waves is studied under the effects of different atmospheric couplings. First, analytical matchings are formulated in which a Rossby wave is coupled to different thermodynamical atmospheres, from a simple heat flux condition to the inclusion of an atmospheric energy balance model. The effects on the vertical structure and phase speed of the first modes are negligible. However, it is shown that for the latter case an unstable mode appears. This growing mode, of decadal period and growth rate, has no physical source of energy and therefore is a result of the oversimplified atmosphere employed. In fact, adding physics to the atmospheric model results in a gradual disappearance of the instability. The possibility of observing similar unphysical modes in climate studies, where oversimplified models are adopted, is raised. Next, a quasi-geostrophic coupled model is used in order to analyse the oceanic Rossby wave characteristics under the influence of a full atmosphere. The idealised eddy-resolving model consists of an ocean basin underneath a channel atmosphere, and different configurations for the oceanic component are used. The Rossby waves are observed to propagate faster than both the classical linear theory (unperturbed solution) and the phase speed estimates when the effect of the zonal mean flow is added (perturbed solution). Moreover, using statistical eigentechniques, a coupled Rossby wave is identified, bearing the characteristics of the coupled mode proposed by Goodman and Marshall (1999). It is argued that the atmospheric coupling is capable of adding an extra speed up to the wave; in fact, when the waves are simply forced, their propagation speed approaches the perturbed solution. The waves are observed to break into faster waves, as suggested by LaCasce and Pedlosky (2004), although their resistance to dissipation and instabilities processes is enhanced by the atmospheric coupling, which provides extra energy to the initial wave during its propagation. The development of a coupled Rossby wave is found to be possible in a basin of the dimensions of both the Pacific and the Atlantic ocean, and its characteristics and strength vary little when the tridimensional accuracy of the ocean is increased.
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