LOCAL WINDS 
height of the ridge were more than twice as large as 
the variations within a similar layer over the plain. 
As a consequence, a pressure gradient from the plain 
to the valley must exist during the day, whereas the 
reverse gradient must appear at night. The equalization 
of pressure differences at the effective ridge altitude 
requires that the pressure differences be largest close to 
the valley bottom and that they decrease with height 
so as to disappear completely at the effective ridge 
altitude. 
From these deductions an adequate theoretical ex- 
planation of the mountain and valley winds can be 
derived. In full accord with observations, the unequal 
rates of decrease in the amplitude of the temperature 
variations over the plain and the valley bottom create 
a pressure gradient of the observed magnitude whose 
direction is toward the valley during the day and away 
from it at night. The air current thus generated fills 
the entire valley and decreases with altitude in accord 
with observations. Thus, there is a thermal cause for the 
pressure differences, and the air current is theoretically 
established as a circulation with a reversal of direction 
at night. This theory also includes the observed circula- 
tion between the plains and the mountains and the 
necessary existence of the upper compensation current. 
Furthermore, the pressure gradient, according to Wag- 
ner, is the result of the combined effects of the inclina- 
tions of valley bottom and ridge line. A nonparallel 
course of these inclinations, such as a downslope of the 
valley bottom and simultaneous upslope of the ridge 
line, would cause an extension of the existing gradient. 
In other words, if the ridge line rises beyond the pass 
altitude toward the neighboring valley, the gradient 
existing in the first valley would run in the same direc- 
tion also in that neighboring valley beyond the pass. 
In this case the wind would reach over the pass as a 
Maloja wind. Thus, this abnormal phenomenon of the 
mountain winds also fits into Wagner’s theory. 
This theory furthermore requires two wind systems 
to preserve the stationary condition in the valley. One 
of them consists of the horizontal inflow of the valley 
wind, produced by the static conditions; the other one 
is the thermal slope wind system which takes care of 
the outflow over the flanking ridges. The combined 
wind systems have an additional effective source of 
energy in the heat given off by the heated slopes. The 
slope winds have a further important function in that 
they continuously add heated slope air to the air over 
the valley through that branch of the slope-wind cir- 
culation which descends over the valley center. Thus, 
the temperature in the center of the valley cross section 
is continuously increased during the day and decreased 
at night, when the heating conditions are reversed. 
The mechanism interlocking the upslope and down- 
slope winds with the mountain and valley winds in the 
course of a day, described in great detail by Wagner 
[73], is shown in Fig. 10. The great importance of the 
thermal slope winds as integral members of the larger 
circulation between plains and mountains is obvious. 
On the basis of a theoretical treatment of the stationary 
slope wind by Prandtl [62], the present author recently 
665 
extended these considerations to the nonstationary 
case [17]. 
Prandtl’s theory has particular significance, because 
a deeper insight into the mechanism of the thermal 
Fie. 10—Schematie illustration of the normal diurnal 
variations of the air currents in a valley. (After F'. Defant [17].) 
(a) Sunrise; onset of upslope winds (white arrows), con- 
tinuation of mountain wind (black arrows). Valley cold, 
plains warm. 
(6) Forenoon (about 0900); strong slope winds, transition 
from mountain wind to valley wind. Valley temperature same 
as plains. 
(c) Noon and early afternoon; diminishing slope winds, 
fully developed valley wind. Valley warmer than plains. 
(d) Late afternoon; slope winds have ceased, valley wind 
continues. Valley continues warmer than plains. 
(e) Evening; onset of downslope winds, diminishing valley 
wind. Valley only slightly warmer than plains. 
(f) Early night; well-developed downslope winds, transi- 
tion from valley wind to mountain wind. Valley and plains at 
same temperature. 
(g) Middle of night; downslope winds continue, mountain 
wind fully developed. Valley colder than plains. 
(h) Late night to morning; downslope winds have ceased, 
mountain wind fills valley. Valley colder than plains. 
slope-wind current was gained through the introduction 
of turbulent heat conduction and turbulent friction. A 
disturbance of the temperature field, as well as static 
instability, always appears in the air layer above a 
heated surface and thus tends to establish turbulence. 
Let us assume the spatial distribution of the potential 
temperature #, together with the temperature disturb- 
ance which stems from the heat transfer along the 
heated slope, in the form: 
8=A+ Bze+ ¥(n), (8) 
