SECT. 2] SMALL-SCALE INTERACTIONS 77 



* 



pointing out that H should be proportional to |i?^|-l/2 j^ a region of forced 

 convection and, according to the theory, a constant independent of Richardson 

 number in a region of free convection. His examination affirmed these relation- 

 ships and gave the constant free convection value of H as about 0.9. The 

 height, Zjn say, at which the region of essentially forced convection merges with 

 the overlying region of essentially free convection, he found to be at the level 

 where \Ri\ reaches a value of approximately 0.03, i.e. 2/«;:i;0.03|L| in terms of 

 Obukhov's scale length, L, defined in formula (15) : the relationship between the 

 two values is 



* 



{Zmi\L\YI'^ = k^ I H (tree convection). 



In a detailed study of observed temperature profiles, Webb (1958) found 

 close agreement wdth the 4/3-power law over a roughly 30-fold height range 

 from 2/|L|=0.03 up to about zl\L\ = l, and found that the gradient ddjdz 

 vanishes at the latter height and remains small or zero in the region above. 

 When the wind is light with a marked lapse, the height at which the 6 gradient 

 vanishes over land or sea is only a few metres; and, correspondingly, Fig. 13 

 (T2— Ts negative, lightest winds) shows that the observed values of ^12.6 — ^4 

 are then close to zero. The wind-profile does not exhibit any related singularity 

 — the trend of du/dz continues smoothly through the transition height where 

 dd/dz vanishes. It seems certain that this transition represents the boundary 

 between the superadiabatic convection layer, of depth a few metres or tens of 

 metres, and the neutral or slightly subadiabatic "homogeneous" region that 

 often extends to a considerable height in the troposphere. 



The homogeneous region has been illustrated by the temperature measure- 

 ments made by Craig (1946, 1947) — see also Craig and Montgomery (1951) — and 

 by Bunker et al. (1949) up to heights of 1000 ft or so over the sea. We must, 

 however, note the difficulty of detecting the superadiabatic layer at these 

 heights, since its potential-temperature gradient would be even smaller there 

 than the 0.2 or 0.3 °F per three-fold height interval which is indicated in Fig. 13. 

 There is a continual buoyant transfer of heat upwards through the neutral or 

 subadiabatic temperature gradient of the homogeneous region, a condition 

 envisaged by Priestley and Swinbank (1947) and treated theoretically by 

 Priestley (1954a). Counter-gradient heat flow in this region has been observed 

 by Bunker (1956). The concepts of transfer coefficient for heat and of Richard- 

 son number cease, of course, to be meaningful in this region. 



As a guide to the height, 2; = | L| , which is approximately where the transition 

 between superadiabatic and homogeneous regions occurs. Fig. 16 shows \L\ in 

 terms of the bulk conditions represented by Bbe. The relationship is somewhat 

 tentative, but should be approximately correct ; it is based on the forms of 

 temperature and wind profiles described below. 



Let us now consider the merging across the boundary between the layers of 

 forced and free convection. As the boundary is approached from beneath, the 

 deviation from the neutral profile may be represented by a function/ as in (16). 



