## Laws of resistance and heat and humidity exchange

We consider the stationary, horizontally homogeneous, stratified PBL. Under stationary conditions the conclusion of constancy with height of the sensible and latent heat eddy fluxes follows from Equations (4.2.3) and (4.2.4). Using this fact and the principle of self-similarity, that is, independence of the developed turbulence regime on molecular constants and characteristics of the underlying surface, Kazansky and Monin (1961) came to the conclusion that the PBL structure should be determined only by u*, H/pcp, E/p, [i and f From this parameter set, two independent combinations with the dimension of length are formulated: the modified Monin-Obukhov length scale L = uI/IkWT* + OMgqJl where T* = (~H/pcp)/ku*, q* = (-E/p)/ku* are temperature and specific humidity scales (see Section 3.9), and the thickness scale A = KuJ\f\ of the neutrally stratified PBL (see Section 4.1) and, respectively, the non-dimensional stratification parameter p0 = ).[L. Thus, if we choose uJk, T*, q* and A as characteristic scales of the mean velocity, temperature, specific humidity and length, respectively, then according to the principle of self-similarity all the non-dimensional statistical characteristics of the developed turbulence regime of the PBL have to be universal functions of two arguments: the non-dimensional height £ = z/L and the stratification parameter p0. In particular, general expressions for defects in velocity, temperature and specific humidity (differences in their values at an arbitrary level z and at the upper boundary hE of the PBL) will take the form

u(z) - G cos a = p0), v(z) - G sin a = (uJk)^^, p0) sign /, e(z)-eh = TMZ,t*o), where \pu, \]/v, ij/g and ij/q are universal functions vanishing at z = hE; 0h and qh are the potential temperature and specific humidity at this level; G and a are moduli of the geostrophic wind velocity and the angle between an isobar and the x axis (see Section 4.1).

Let us turn now to a derivation of the laws of resistance and heat and humidity exchange connecting characteristics (u^, a, 7^, q^) with the external parameters of the PBL. For this purpose we take advantage of the procedure of an asymptotic matching which allows for the existence of the so-called overlapping region where Equations (4.3.1) for the outer part of the PBL at small c coincide with the expressions

"(z) = ("*/*•") In z/z0, v(z) = 0, 0(z) - 0O = (^/ccg) In z/z0, <?00 -q0 = (<2*/<) In z/z0,

for the surface atmospheric layer at large z/z0. Carrying out the given requirement (combining Equations (4.3.1) and (4.3.2)) we obtain

iPo) sign/

0 0