Circulation transformed Eulerian mean

Lagrangian Mean, Diabatic, and Transformed Eulerian Mean Circulations... 

It defines the transformed Eulerian mean (TEM) or residual circulation. When these definitions are applied to the simplified form (3.63) of the thermodynamic equation, the resulting circulation is called the diabatic circulation and the meridional and vertical velocities will be noted (vd,wd) rather than (v, w ). In this case, the simplified thermodynamic equation and the steady state approximation for the continuity equation become... 

It is important to note that the diabatic circulation can be estimated from the thermodynamic and continuity equations only if the temperature distribution is known a priori. However, a fully self-consistent mean meridional circulation can be obtained when the momentum budget is considered together with the thermodynamic and continuity equations. When transformations (3.64a, b) are applied to the zonal mean equations (3.53-3.60), the solution of the following momentum, continuity, and thermodynamic equations defines the transformed Eulerian mean (TEM) or residual circulation (here expressed in log-pressure coordinates) ... 

Figure 3.23. Mass streamfunction for the transformed Eulerian mean circulation (109kg/s) calculated by Becker and Schmitz (2002) for the month of January. Compare this residual circulation with the Eulerian mean circulation shown in Figure 3.21.

The conceptual advantage of the diabatic or transformed Eulerian mean circulations is that the eddy-mean flow cancellation is avoided, and a first approximation to the net meridional and vertical transport needed for atmospheric studies is therefore readily obtained. The most important features of this transport description are that air generally enters the lower stratosphere in the tropics and exits at middle and high latitudes in both hemispheres. In the upper stratosphere and mesosphere, air flows from the summer hemisphere to the winter hemisphere, and downward near the winter pole. This transport description is qualitatively very similar to that proposed by Brewer based... 

The formalism of the transformed Eulerian mean circulation shows that meridional transport in the middle atmosphere is generated primarily by non-local momentum forcing associated with wave dissipation. This forcing, represented by the Eliassen-Palm flux divergence in equation (3.67), acts as an extratropical pump producing strong upward air motions in the tropics and downward return ... 

Figure 3.27. Schematic representation of the global diffuser model (upper panel) and tropical pipe model (lower panel). Gray arrows denote meridional transport by the transformed Eulerian mean circulation while the heavy solid arrows show quasi-horizontal mixing by large scale waves. The vertical lines in the lower panel represent dynamical barriers against meridional transport in the tropics. From Plumb and Ko (1992).

Juckes, M., A generalization of the transformed Eulerian-mean meridional circulation. 

The sections of this chapter deal with the following elements of atmospheric dynamics vertical structure of the atmosphere (Section 3.2), fundamental equations of atmospheric motions (Section 3.3), transport of chemical constituents and the relative importance of dynamical and chemical effects on photochemical species (Section 3.4), atmospheric waves (Section 3.5), the mean meridional circulation and the use of the transformed Eulerian formalism to illustrate the roles of mean meridional and eddy transports (Section 3.6), the important role of wave transience and dissipation (Section 3.7), vertical transport by molecular diffusion in the thermosphere (Section 3.8), and finally, models of the middle atmosphere (Section 3.9). 

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