Diabatic circulation

Stordal, F lsaksen, I.S.A. and Homtvedt, K. (1985). A diabatic circulation two-dimensional model with photochemistry Simulations of ozone and long-lived tracers with surface sources. J. Ceophys. Res., 90, p. 5757-5776. 

Marcus model and diabatic states make more immediate (even if not strictly necessary) the introduction of the dynamical solvent coordinate, of which in Section 5.2 we have given a definition based on parameters of the continuum model, but other definitions are possible. Actually, the Russian school used this concept without giving formal definitions, at the best of our knowledge (several papers have been published in relatively minor Russian journals, with limited circulation in western countries in those years), and basing it on a description of the solvent as a continuum or a set of os-... 

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

A more practical approach is simply to derive the net mean circulation directly from the diabatic heating rate, q, as suggested by Dunkerton (1978). From the thermodynamic equation (3.60) in which it is assumed that d /dt and (v/a)(dO/dheat fluxes are negligibly small, one can deduce that... 

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) ... 

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... 

Hasebe, F., Quasi-biennial oscillations of ozone and diabatic circulation in the equatorial stratosphere. J Atmos Sci 51, 729, 1994. 

Haynes, P.H., C.J. Marks, M.E. McIntyre, T.G. Shepherd, and K.P. Shine, On the downward control of extratropical diabatic circulation by eddy-induced mean zonal... 

Huang, T.Y.W., and A.K. Smith, The mesospheric diabatic circulation and the parameterized thermal effect of gravity wave breaking on the circulation. J Atmos Sci 48, 1093, 1991. 

Mlynczak, M.G., C.J. Mertens, R.R. Garcia, and R.W. Portman, A detailed evaluation of the stratospheric heat budget, 2. Global radiation balance and diabatic circulations. J Geophys Res 104, 6039, 1999. 

In general equation (23b) is not satisfied so that rigorous diabatic bases do not exist. As a consequence, (R), determined from equation (22), is path dependent and the circulation of f (R), the line integral of f (R) along a closed loop, does not vanish. Equation (23b) is difficult to evaluate numerically. However, the circulation of f is comparatively easy to evaluate and provides a computationally attractive, and in view of equation (22) an intuitively appealing, alternative to equation (23b). This point is discussed further in Section 6.5 and is addressed numerically in Section 8. 

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