Variation of Wind with Height in the Atmosphere

The atmosphere near the surface of the Earth can be divided into three layers—the free atmosphere, the Ekman layer, and the surface layer. The Ekman layer and the surface layer constitute the so-called planetary boundary layer. The Ekman layer extends to a height of from 300 to 500 m depending on the type of terrain, with the greater thickness corresponding to the more disturbed terrain. 

In the Ekman layer, the wind direction tends to turn clockwise with increasing height in the Northern Hemisphere (counterclockwise in the Southern Hemisphere). The wind speed in the Ekman layer generally increases rapidly with height however, the rate lessens as the free atmosphere is approached. The exact distribution of the wind speed depends on many parameters, particularly the vertical distribution of the horizontal pressure gradient as well as the atmospheric stability. 

The layer immediately adjacent to the surface, typically up to 30 to 50 m from the ground, is called the surface layer. Within this layer, the vertical turbulent fluxes of momentum and heat are assumed constant with respect to height, and indeed they define the extent of this region. 

In this section we consider the prediction of the variation of wind with height in the surface and Ekman layers. Most of our attention will be devoted to the surface layer, the region in which pollutants are usually first released. 

One other item should be discussed before we begin, and that is the question of smooth versus rough surfaces. In meteorological applications, the surface features leading to roughness are usually so closely distributed (e.g., grass, crops, bushes) that only the height 

Knowledge of the governing physics of flows in the surface layer is not sufficiently complete to derive the vertical mean velocity profiles based on first principles. Useful empirical relationships have been developed using approximate theories and experimental measurements. Similarity theories, based on dimensional analysis, provide a convenient method for grouping of the system variables into dimensionless parameters and then the derivation of universal similarity relationships. 

1 Mean Velocity in the Adiabatic Surface Layer over a Smooth Surface 

Consider first the steady, ground-parallel flow of air over a flat homogeneous surface. We assume that the wind flow is in the x direction (uy = 0) and that ux = ux(z). Our goal is to determine ux(z) assuming that the vertical temperature profile is adiabatic. 

The Buckingham 7t theorem states that in this system there are only 5 — 3 = 2 independent dimensionless groups, and 7t2, relating the five variables, so that F(jti,7t2) = 0. The 7t theorem does not tell us what the groups are, only how many exist. As the first group we select 

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VARIATION OF WIND WITH HEIGHT IN THE ATMOSPHERE 871 where = ZqIL. Huang (1979) has presented F(<, o) as... 

Concentrations of contaminants in the atmosphere may vary significantly from time to time due to seasonal climatic variation, atmospheric turbulence, and velocity and direction of wind. The most important meteorological factors are (1) wind conditions and the gustiness of wind, (2) the humidity and precipitation, (3) the temperature, which varies with latitude and altitude, (4) barometric pressure (varying with the height above the ground), and (5) solar radiation and the hours of sunshine, which vary with the season. 

The pressure of the air, as already mentioned, varies with altitude indeed, at one and the same place it does not remain constant in consequence of variation m composition, the influence of wind, etc. A standard pressure, known as an atmosphere, has been chosen. The British unit is a column of mercury 29-905 inches in height, measured at 82° F. m London, and is equivalent to a pressure of 14-78 lb. per square inch. 

Earth s atmosphere is divided into five layers based on altitude and temperature variation. The lowest layer—the troposphere—extends from Earth s surface to a height of approximately 15 km, as shown in Figure 26-1. Temperatures in the troposphere generally decrease with increasing altitude, reaching a minimum of —58°C at 12 km. Rain, snow, wind, and other weather phenomena occur in this layer. We live our entire lives within the troposphere. Only astronauts in spacecraft go beyond its reach. 

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