Ixra M[2521

Integrating (2.5.21) over the entire mass of the atmosphere and taking into account appropriate boundary conditions, we have jt j Kua2 cos cp dA dcp dp/g = C(AM, KM) + C(KE, KM) - D(KU), (2.5.22)

where

D(Km) = - J (M[FJ + [i>][F,])a2 cos <p dX d<p dp/g. (2.5.25)

To derive the budget equation for KE we direct our atttention again to the primitive atmospheric dynamics equations, Equations (2.5.16)—(2.5.19). Multiplying the first of these equations by u, and the second by v, and then adding the resulting expressions, and using the two remaining equations of the system, Equations (2.5.16)—(2.5.19), we obtain the local equation of the kinetic energy budget for the total (zonal mean plus eddy) motion. This takes the form du2 + v2+ 1 / d fu2 + v2 \ d iu2 + v2 v cos \\ | d (u2 + v2 m dt 2 acos<p\d/i.\ 2 J d<p\ 2 // dp\ 2

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