SECT. 2] SMALL-SCALE INTERACTIONS 79 



dicates for the wind-profile, Zml\L\ =0.032 and correspondingly H (free convec- 

 tion) = 0.94. As these are, to within experimental error, eqnal to the values of 



« 



Zmj\L\ and H obtained directly from observed temperature-profiles and heat 

 fluxes as mentioned above, this seems to justify the trial assumption of ai = 4.5. 

 This assumption implies, of course, the virtually exact similarity of wind- and 

 potential temperature-profiles over a range extending from the forced convec- 

 tion region into at least part of the free convection region, and, throughout 

 this range, we would, therefore, have KhIKm= 1. This disagrees with the in- 

 dication from eddy-correlation results that KhIKm is greater than unity over 

 the whole unstable range ; and further work is needed to clarify the differences 

 between wind- and temperature-profiles. Assumed similarity between the two 

 profiles leads to a curve of Km against Ri rather similar to that shown in 

 Fig. 2 from Ellison's formula but running about 15% higher in the Ri range 

 — 0.2 to —0.4; it is clear that measurements of shearing stress are not yet 

 sufficiently numerous or refined to arbitrate between the two. 



One of the possible alternative approaches to this problem is through the 

 examination of humidity -profiles, and of particular value in this direction will 

 be measurements over the sea, where the surface condition is highly uniform 

 and it is possible to secure a large fetch. The point here is that the humidity- 

 profile is in some respects more amenable to accurate and representative 

 measurement than is the wind-profile; and all the evidence is concordant, as 

 mentioned earlier, in indicating that the two are effectively identical in form. 



Just one further remark may be made regarding the form of the humidity- 

 profile. In the upper parts of the free convection region, the supposed mechan- 

 ism of the vanishing potential-temperature gradient (Webb, 1958) implies 

 that the humidity-profile probably follows fairly closely the form of the poten- 

 tial temperature-profile, including a similar abrupt fall to negligible gradient 

 at about z= \L\. No observations relating to this are yet available, however. 



/. Inversion Conditions 



As inversion conditions over land are accompanied by low wind velocities 

 and considerable unsteadiness associated with katabatic drifts, etc., observa- 

 tional difficulties have hampered progress and little is known with certainty. 

 Over the sea, steady conditions of inversion are more frequently encountered 

 particularly in coastal waters, with a warm wind from the land blowing over 

 cooler sea. 



The observations of Pasquill (1949) and Rider (1954) have indicated that the 

 equality of the transfer coefficients for momentum and water vapour. Km and 

 Ke, extends to inversion conditions. It is therefore to be expected that the 

 Rossby-Montgomery stability relationship (17) should apply to the humidity 

 profile if u and u^ are replaced by q and Ejpu^ respectively and a value cr = 9 

 used as for the wind-profile. The relationship would thus be 



Ke = kj{l + aRiy/^. (38) 



