TLIWHIILENT ATMOSPHERK’ DIFFUSION
5
instruiiients measure a constant velocity. some others will manifest very
rapid fluctuations around the mean velocity. Two recordings of wind velocity by a cup anemometer and a hot-wire anemometer look at first glance
very different. The gusts lasting less than a few seconds completely disappear
in the cup anemometer recording; on the contrary they appear as very sharp
peaks on the hot-wire recording. Magnan (1931; Huguenard er al., 1924,
1928), who was the first. in 1929, to use systematically the hot-wire
anemometer in the atmosphere near the ground, has detected fluctuations of
the wind velocity, which were completely smoothed by the cup anemometer;
to give only one example. on the seashore (isle de Ri) he has observed a wind
velocity increasing from 12 to 21 m/sec in a time of j sec.
In the kinetic theory the velocity fluctuations about their mean value (the
velocity of the continuous medium) are attributed to the molecules; in a
turbulent flow it is much more difficult to give a precise formulation; the role
of the molecules has to be played by cells ‘ * or , , balls ” of some sort, which
one calls “eddies.” It is remarkable that thc first paper of Sir Geoffrey Taylor
(1915a) on atmospheric turbulence has as its title, “Eddy diffusion in the
atmosphere”; but one “eddy” cannot have a sharp definition, like a
molecule of the kinetic theory; when at the point x, y, z at time t one records
a velocity fluctuation
u’(.v, .Y, i, I),
~ ‘ ( x .
y, Z, t),
w’(x, y, I, r )
this is interpreted as the passing of one eddy, a ball of fluid rotating around a
center, this center moving with the mean velocity
ir(x, y, 2, t ) ,
v(x, y. 2, t).
“(x, y, z, I )
Hut the analogy must not be pressed to much; the molecules-at least in the
niiw VICW of classical kinetic theory are permanent objects and their energy
can change only by collisions; the balls, rolling around themselves, which
arc callcd eddies, have no sharp boundaries and their energy is continually
changing; nevertheless these rather fuzzy objects gave a significant meaning
to the “scale of turbulence‘’ which is fundamental for any interpretation of
turbulent atniospheric diffusion. The scale is roughly defined by the
dianicter of the eddies, whose influence is predominant on the scattering of
the material under consideration. Dedebant and WehrlS (1935) have placed
great emphasis on this point of view; for instance, in the diffusion of the
smoke of a chimney the significant eddies might have an average diameter of
one meter (Dobson, 1919); for the diffusion of pollen over the Baltic sea, this
average diameter might be several hundred meters (Schmidt, 1925); for the
diffusion over the whole earth of the particles blown up by the Krakatoa,
eddies figuring the general circulation of the atmosphere were responsible.
It was only when spectral analysis (in time and space) of the turbulent
5
instruiiients measure a constant velocity. some others will manifest very
rapid fluctuations around the mean velocity. Two recordings of wind velocity by a cup anemometer and a hot-wire anemometer look at first glance
very different. The gusts lasting less than a few seconds completely disappear
in the cup anemometer recording; on the contrary they appear as very sharp
peaks on the hot-wire recording. Magnan (1931; Huguenard er al., 1924,
1928), who was the first. in 1929, to use systematically the hot-wire
anemometer in the atmosphere near the ground, has detected fluctuations of
the wind velocity, which were completely smoothed by the cup anemometer;
to give only one example. on the seashore (isle de Ri) he has observed a wind
velocity increasing from 12 to 21 m/sec in a time of j sec.
In the kinetic theory the velocity fluctuations about their mean value (the
velocity of the continuous medium) are attributed to the molecules; in a
turbulent flow it is much more difficult to give a precise formulation; the role
of the molecules has to be played by cells ‘ * or , , balls ” of some sort, which
one calls “eddies.” It is remarkable that thc first paper of Sir Geoffrey Taylor
(1915a) on atmospheric turbulence has as its title, “Eddy diffusion in the
atmosphere”; but one “eddy” cannot have a sharp definition, like a
molecule of the kinetic theory; when at the point x, y, z at time t one records
a velocity fluctuation
u’(.v, .Y, i, I),
~ ‘ ( x .
y, Z, t),
w’(x, y, I, r )
this is interpreted as the passing of one eddy, a ball of fluid rotating around a
center, this center moving with the mean velocity
ir(x, y, 2, t ) ,
v(x, y. 2, t).
“(x, y, z, I )
Hut the analogy must not be pressed to much; the molecules-at least in the
niiw VICW of classical kinetic theory are permanent objects and their energy
can change only by collisions; the balls, rolling around themselves, which
arc callcd eddies, have no sharp boundaries and their energy is continually
changing; nevertheless these rather fuzzy objects gave a significant meaning
to the “scale of turbulence‘’ which is fundamental for any interpretation of
turbulent atniospheric diffusion. The scale is roughly defined by the
dianicter of the eddies, whose influence is predominant on the scattering of
the material under consideration. Dedebant and WehrlS (1935) have placed
great emphasis on this point of view; for instance, in the diffusion of the
smoke of a chimney the significant eddies might have an average diameter of
one meter (Dobson, 1919); for the diffusion of pollen over the Baltic sea, this
average diameter might be several hundred meters (Schmidt, 1925); for the
diffusion over the whole earth of the particles blown up by the Krakatoa,
eddies figuring the general circulation of the atmosphere were responsible.
It was only when spectral analysis (in time and space) of the turbulent