A review is given of relevant work on the internal boundary layer (IBL) associated with:
 The major theme in all cases is on the downstream, modified profile form (wind and temperature), and on the growth relations for IBL depth.

The internal boundary layer — A review

An easily-evaluated expression for the dimensionless concentration profile χ(z/z0,χ/z0, z0/L) = = cu*/kQ (or z0cu*/kQ) downwind of a continuous ground-level area (or line) source in the stable surface layer is obtained by integrating the diffusion equation using the Shwetz approximation method (c = concentration, Q = source strength, k = von Karman's constant). The analytical solution compares closely with concentration profiles obtained using a trajectory-simulation model over a useful range of heights, the important discrepancies occurring at the upper edge of the plume. The analytical solution is used to generate predictions of ground-level concentration for the Project Prairie Grass experiments; good agreement with the observations is obtained at all downwind distances (50 to 800 m).

/pdf/an-approximate-analytical-solution-to-the-diffusion-equation-39kxldrwn2.pdf

An approximate analytical solution to the diffusion equation for short-range dispersion from a continuous ground-level source

The effect of local advection on evaporation and Bowen ratio over alternating crosswind infinite dry-warm and wet-cool surface strips (patches), by redistribution of surface heat, is analysed. The analysis shows that evaporation over the region is enhanced by local advection, as observed experimentally by other researchers. Results suggest that evaporation can be enhanced more than 10% or 20% by local advection on the area covered by patches smaller than 10tu Ūd m or 5tuŪd m, respectively, where tu is a unit time and Ūd the mean wind velocity in the internal boundary layer. This means that the traditional first-order approximation of surface energy balance, without considering local advection, might lead to significant error for such small-scale inhomogeneity. It may, however, be applicable to large patches (≫)10tu Ūd m, where energy partition may then be directly approximated from area-weighted averages of properties derived from extended wet and dry surfaces, according to the patchy area fracti...

An Analysis of the Effect of Local Heat Advection on Evaporation over Wet and Dry Surface Strips

Some comparisons between mixing-length and turbulent energy equation models of flow above a change in surface roughness

Experimental results of the drag-coefficient estimation for air-coast interfaces

A review is presented of some Russian-language papers published as early as 1952–1954 that are unknown to most English-speaking readers. In these papers the influence of an abrupt change in the surface friction velocityv*, surface roughnessz0 and surface temperature or heat flux on the wind velocity profile and vertical motions has been investigated analytically and numerically. Most of the theories are based on the exchange-coefficient approximation for momentum and heat. In terms of this approximation, further generalization and development of the problem is discussed.

E. Donev

Papers

Wind profile and vertical motions above an abrupt change in surface roughness and temperature