WIND ENERGY SYSTEMS - Cd3wd

Chapter 2—Wind Characteristics 2–19
On clear nights, however, the earth will be colder than the air above it, so a parcel at the
temperature of the earth that is displaced upward will find itself colder than the surrounding
air. This makes it more dense than its surroundings so that it tends to sink back down to
its original position. This condition is referred to as a stable atmosphere. Atmospheres which
have temperature profiles between those for unstable and stable atmospheres are referred to
as neutral atmospheres. The daily variation in atmospheric stability and surface wind speeds
is called the diurnal cycle.
It is occasionally convenient to express the actual temperature variation in an equation
similar to Eq. 10. Over at least a narrow range of heights, the prevailing temperature T p (z)
canbewrittenas
T p (z) =T g − R p (z − z g ) (11)
where R p is the slope of a straight line approximation to the actual temperature curve called
the prevailing lapse rate. T g is the temperature at ground level, z g m above mean sea level,
and z is the elevation of the observation point above sea level. We can force this equation to
fit one of the dashed curves of Fig. 10 by using a least squares technique, and determine an
approximate lapse rate for that particular time. If we do this for all times of the day and all
seasons of the year, we find that the average prevailing lapse rate R p is 0.0065 o C/m.
Suppose that a parcel of air is heated above the temperature of the neighboring air so it
is now buoyant and will start to rise. If the prevailing lapse rate is less than adiabatic, the
parcel will rise until its temperature is the same as the surrounding air. The pressure force
and hence the acceleration of the parcel is zero at the point where the two lapse rate lines
intersect. The upward velocity, however, produced by acceleration from the ground to the
height at which the buoyancy vanishes, is greatest at that point. Hence the air will continue
upward, now colder and more dense than its surroundings, and decelerate. Soon the upward
motion will cease and the parcel will start to sink. After a few oscillations about that level
the parcel will settle near that height as it is slowed down by friction with the surrounding
air.
Example
Suppose that the prevailing lapse rate is 0.0065 o C/m and that a parcel of air is heated to 25 o C
while the surrounding air at ground level is at 24 o C. Ground level is at an elevation 300 m above sea
level. What will be the final altitude of the heated parcel after oscillations cease, assuming an adiabatic
process?
The temperature variation with height for the linear adiabatic lapse rate is, from Eq. 10,
T a =25− 0.01(z − 300)
Similarly, the temperature variation for the prevailing lapse rate is, from Eq. 11,
T p =24− 0.0065(z − 300)
Wind Energy Systems by Dr. Gary L. Johnson November 20, 2001