## Ya 7

Let us obtain the budget equations for KM and KE. At first, we move from coordinates X, cp, z and t to isobaric coordinates X, cp, p and t. Then the atmospheric dynamics equations, Equations (2.5.1)—(2.5.3), are written in the form u du v du du („ u \ 1 ¿>®

H----l-oj — — I / + - tan cp )v = —--+ Fx, a dcp dp \ a J a cos q> dX

a cos cp \d2. d(p / dp where co = dp/dt is the isobaric vertical velocity; a = 1/p is the specific air volume; Fx and Fv are the components of the vector F in the direction of axes X, (p; f = 2Q sin <p is the Coriolis parameter; the remaining designations are the same.

Rewriting Equations (2.5.16) and (2.5.17) in divergent form and averaging them over longitude we have d 1 <5 r i /-r -, r -, tan (p t- M +-t- luv] cos cp + — [uco] - /[i7] - [up]-= [FJ, ot a cos <p dcp dp a d r n 1 d r 2n ^ r t yr n r 2n tan <P

Let us substitute the definitions of u, v and co from (2.5.1) into these equations and then multiply the first by [u], the second by [p] and add the resulting expressions. After these transformations we have d i/r,n2 , r,n2\ , 1 J r„n ^ /Yr,.ir,n , r„*„*i

+ M ^ ((M2 + [p*2]) COS cp) j + j[u] - ([«][«] + lu*a>*])

+ M ^ (MM + [p*(0*])j - ([u*p*][u] - [u*2][p]) ^ dp J a

Let us present the second and third terms on the left-hand side and the first term on the right-hand side of this equation in the form

a cos cp I dcp

dcp J a cos cp Idcp

+ [u*p*][u] + [p*2][p]j cos cp^j - cos <p^[u*p*] ^ + [p*2] f^)};

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