In z + C; /c _*,5c =-ln—î + Cl (3.6.5) clku^ \ v / a v where a is a numerical constant of order unity; C is the constant of integration defined by the condition of equal concentrations joining at the boundary with the underlying layer and thereby depending on the concentration change in the thin near-wall layer; Cl = (F0/pKUj),)~1C — a"1 In u^/v.
To estimate the constant C, several methods have been proposed. The simplest of these is to use the Reynolds hypothesis (or, as it is often called, the Reynolds analogy) about the identity of mechanisms of the momentum and admixture transfer in a layer of approximate constancy of fluxes. This is equivalent to assigning the relation
where wl5 u2 and cl5 c2 are values of the mean velocity and admixture concentration at two fixed heights.
Comparing (3.6.3) to (3.2.8), and (3.6.5)—(3.2.12), we see that the relation mentioned above is fulfilled only at Sc = 1, a = 1 in the entire boundary layer including the viscous-buffer layer. In other words, its introduction is equivalent to discounting changes in admixture diffusion affected by the molecular Schmidt number. The latter amounts to 0.62 for water vapour.
Turning to discuss admixture diffusion near a rough wall, we note that the Reynolds analogy in this case is not fulfilled in general because the momentum exchange does not now depend on viscosity, and the diffusion continues to be controlled by molecular transfer. In such a situation there is nothing to be done but to present an expression for the profile of the admixture concentration in the form where ac is inversely proportional to the turbulent Schmidt number (see below), and then to use empirical data (say, data from laboratory experiments) to determine the parameter Sc0 meaning a near-surface concentration jump. Based on dimensional considerations it was shown by Yaglom and Kader (1974) that, for temperature, the numerical parameter SQq/T^ (here, = —H/pcpKU# is the temperature scale) is a function of the surface Reynolds number Re0 and is associated with it by the relation
But because the discussion has turned to temperature, it is worth remembering that its identification with a passive admixture, strictly speaking, has no justification due to the appearance in heated liquids of additional buoyancy forces and the dependence of molecular viscosity and thermal conductivity on temperature.
3.7 Coefficients of resistance, heat exchange and evaporation for the sea surface
We have already mentioned the sea surface resistance coefficient several times. And now it is time to explain its meaning, and that of the heat exchange and evaporation coefficients related to it. We give the names resistance coefficient, heat exchange coefficient (Stanton number), and evaporation coefficient
(Dalton number) to non-dimensional integral characteristics of momentum, heat and moisture exchange defined, respectively, as
Here 60 and q0 are temperature and air specific humidity at the underlying surface; u, 0 and q are the mean wind velocity, temperature and specific humidity at a fixed height z.
According to these definitions and Equations (3.4.1) and (3.6.5) describing the vertical distributions of the mean wind velocity and an arbitrary passive admixture in the logarithmic boundary layer, the expressions for C„, C0 and Cq can be presented in the form
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