where the factor sign f in the second formula, as well as in Equation (4.3.1), takes into account the opposite directions of rotation of the velocity vector in the Northern and Southern Hemispheres.

Further, because the right-hand sides of Equations (4.3.3) are functions of but the left-hand sides are not, then to satisfy these equalities it is necessary for their right-hand sides to approach non-zero finite limits depending only on Ho at small values of the argument Therefore, we introduce the following definitions:

lim|>u(£, ¡x0) - In £] = B(n0) + In k, i-o lim n0) = A(n0), lim [o$il/B(Z, n0) - In £] = C(hq) + In k, o ho) - In £] = D(p0) + In k,

I-o where A, B, C and D are the non-dimensional universal functions of the argument ju0. Then taking into account the facts that In X/z0 = ln(KM^./G)(G/|/|z0) = In (ku^/G) + In Ro, where Ro = G/|/|z0 is the Rossby number, and that on the basis of the second equality in (4.3.3)

cos a = (1 - sin2 a)1/2 = (iuJkG)\k\uJG)~2 - A2(n0)Y/2

we find


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