A modified Lagrangian-mean (MLM) diagnostics of tracer transport in the stratosphere developed by Nakamura(1995) is extended to study the low-frequency variations of the troposphere from a viewpoint of mass conservation. Our method describes the time variation of mass in a volume element enclosed by two nearby surfaces of potential vorticity (PV) and those of potential temperature in terms of nonconservative mass flux through these surfaces. A long time-mean of the MLM mass flux illustrates a direct meridional circulation without eddy flux contributions under the constraints of both dynamics and thermodynamics.
Low-frequency variations of the zonal mean zonal flow and baroclinic eddies in a simple global circulation model, of which dynamics were investigated in the previous paper by the authors (Akahori and Yoden, 1997), are diagnosed by the new method. A characteristic feature is a propagation of the MLM mass anomalies from the tropics to the polar region with a time-scale over 100 days, which sets in rather periodically with a shorter time-scale. The poleward propagation of the mass anomalies is related to that of the zonal-flow anomalies, already found in some observational and numerical studies.
In low latitudes, the mass anomaly is mainly induced by the convergence of the meridional mass flux through PV surfaces, which is related to anticyclonic Rossby-wave breakings in the upper troposphere. In midlatitudes, on the other hand, it is largely induced by the convergence of the vertical mass flux through isentropic surfaces, which is related to the thermal relaxation. In high latitudes, cyclonic Rossby-wave breakings on the poleward flank of the jet stream become important for the mass anomaly. Rather periodic occurrence of such propagation of the mass anomalies are characterized by a kind of relaxation oscillation which consists of a phase of mechanical mixing by Rossby-wave breakings and a recovery phase due to thermal forcing.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics