A multiscale theory of convective momentum transport in the tropical atmosphere

Abstract: A multiple-scales asymptotic framework is employed to analyze the interaction between a field of small-scale convective circulations and the large-scale tropical circulation. Closed equations governing the large-scale flow are derived, providing a systematic closure for the influence of unresolved convection. The influence of unresolved convection enters through a non-local momentum diffusion operator that provides a first-principles representation of convective momentum transport and naturally couples the vertical baroclinic modes of the large-scale circulation. The classical Matsuno--Gill model is recovered as a limiting approximation in which the derived momentum transport operator reduces to the phenomenological damping introduced by Gill, thereby placing the classical theory on a systematic first-principles foundation. Two applications of the generalized theory are considered. First, steady-state circulations driven by localized equatorially symmetric heating are examined. Convectively induced vertical-mode coupling is shown to excite additional baroclinic modes beyond those directly forced, substantially modifying the vertical structure of the Walker circulation. Second, the equatorial wave spectrum is analyzed. The resulting eigenmodes comprise mixtures of the classical equatorial wave families, causing the dispersion relations to lose their distinct branch structure and exhibit systematic frequency shifts. These results demonstrate how convectively induced momentum transport systematically modifies both steady tropical circulations and equatorial wave dynamics.