Tropical-Midlatitude Rossby Wave Coupling in the Presence of an Overturning Meridional Circulation

Abstract:

While interactions between atmospheric waves and mean zonal flows have been the focus of extensive research, the same cannot be said of the dynamics of waves in the presence of purely meridional background flow. In the deep tropics, though, where the mean zonal flow nearly vanishes, such dynamics are of central importance. Based on the Intraseasonal Multiscale Moist Dynamics (IMMD) system of Biello and Majda (2010), a simplified set of equations describing the behavior of equatorial atmospheric waves in the presence of a planetary-scale overturning meridional-vertical circulation were derived. The IMMD's scaling is appropriate to describe zonally-long anomalies around a mean climatology and thus provides a framework to study the Madden-Julian oscillation. The result of the present derivation is a coupled two-layer equatorial shallow water system, the solutions of which--planetary and equatorially trapped Rossby waves--do not interact in the absence of the background circulation but resonate under certain conditions for nonzero meridonal/vertical background flow; this coupling suggests a mechanism for energy exchange between the tropical atmosphere and that of the middle latitudes. In the absence of diffusion the coupled system is Hermitian, and therefore all solutions are stable; in contrast to wave stability in the presence of zonal shear flow this point is particularly striking. For all numerical computations the prescribed background circulation mimics the vertical and meridional components of the Hadley cell, the dominant structure of large-scale equatorial atmospheric flow. Numerical results for small diffusion include the slowing, but lack of dissipation, of equatorial Rossby waves and the robustness of the equatorial Kelvin wave.