The effect of potential vorticity fluxes on the circulation of the tropical upper troposphere

With simple analytical arguments, we suggest that the subtropical westerly jets, the equatorial easterly winds, the westerly ducts (i.e. regions of westerly winds over the Equator), and the tropical upper tropospheric troughs, are coupled via potential vorticity (PV) dynamics. We suggest that deep tropical convection leads to advective PV fluxes towards the Poles over the subtropical westerly jets, triggering Rossby waves on the jet, and leading to advective PV fluxes towards the Equator when the Rossby waves break over the westerly ducts. Moreover, we show that the advective PV fluxes towards the Poles closely balance those towards the Equator, and suggest that this close balance is to be expected from the impermeability theorem. We then argue that small imbalances of these advective PV fluxes play an important role in maintaining the upper tropospheric mean flow of the tropical atmosphere. We test our ideas using a shallow-water model of the atmosphere, where diabatic heating terms are absent, and show how imbalances in the advective PV fluxes of a shallow-water model maintain its mean flow. We focus on the periodicity of the shallow-water models to study the effect of transient eddies and relate our results to previous studies.