We have analysed the temporal variation of the seeing in order to have a better
insight into the atmospheric behaviour which gives rise to optical turbulence.
Recently a number of phenomenological processes have been described
(Coulman et al. 1996). In this paper, it is assumed that optical turbulence
is
concentrated in twin laminae (very thin turbulent layers 
m)
which appear on top and at the bottom of a unique thick mechanical turbulent
layer (
m). The authors of that paper suppose that in the greater part of the atmosphere
the critical Richardson number (
) is not attained
and that turbulent conditions are triggered by localized gravity waves
which appear suddenly and then propagate with oscillatory behaviour.
From the point of view of astronomers it would be convenient to be able to have a characterization of the temporal evolution of the seeing, i.e. to know what the typical time interval of seeing variation is, and also the dependence of seeing quality with time, if any. With this information one can conceivably optimize astronomical facilities. Up to now no general laws have been established.
In Fig. 7 (click here) the result of averaging all observing nights is shown versus UT and no general trend in the seeing evolution is observed. This is an important conclusion which can be opposed to the generally accepted assumption that "seeing is worst at the beginning of the night''. Our measurements are free of local disturbances that occur in telescope buildings which, in the best cases, reach thermal equilibrium after several hours.
Figure 7: Averaged seeing versus
UT for the entire observing period at site A (nine months)
Inspecting individual nights, it can be observed that during relatively stable nights, with good seeing (0.5'' typical mean values), the seeing can deteriorate over short periods. One can clearly see, as is shown in Fig. 8 (click here), in the middle of the night, a steep rise in the seeing from less than 0.5'' up to more than 2'' in less than 10 minutes. After this burst, one or two hours are necessary for good image quality to be recovered. This can be interpreted by saying that even under good seeing conditions and hence quasi-laminar flow, the steady equilibrium can be broken by a perturbation and degenerate into turbulence within a few minutes.These assumptions are supported by the fact that we never noticed an abrupt seeing improvement (the sequence is not reversible).
Figure 8: Seeing versus UT on the night of
1995 May 4 at site A
Another pattern that may occasionally appear in the temporal evolution of seeing
is
shown in Fig. 9 (click here) in which an oscillatory behaviour
is observed. Also in this figure the corresponding autocorrelation
function is
shown for time intervals ranging from 
0 to 4 hr. The
plot of Fig. 9 (click here)b ends at 4 hr. For longer time intervals, the number of measurements during a single
night is not sufficient for the autocorrelation function to make sense. From
Fig. 9 (click here)b a 45-min periodic variation is visible.
Superimposed on this oscillation, one can note also a slow
decrease and after a 3-hour delay no correlation remains.
Figure 9: a) Seeing versus UT on the
night of
1995 May 10 at site A; b) autocorrelation function corresponding to
the same night
As pointed out previously, the presence of longer time-interval correlations cannot be studied through single-night observations. Moreover we are also interested in the possible presence of a universal temporal behaviour of seeing to be interpreted in more general theories concerning turbulence phenomena. For so doing we analysed the averaged autocorrelation function, computed over all the available data during the nine months (Fig. 10 (click here)). We have discarded the nights with less than 6 hours of observations. Each individual daily correlation has been centred and normalized to the mean seeing:
where i index refers to individual night. No oscillations seem to remain in the correlation and therefore a large spectrum of (gravity) waves might be present in the atmosphere. For small time delay, the correlation closely follows an exponential decay with a T = 1.2-hr time constant.
Figure 10:
Averaged autocorrelation function considering all the measurements. Superimposed, with a continuous line, is the best fit
with A = 0.071.
As mentioned before, if one assumes that the seeing is the superimposition of many individual exponential decay functions of the type
for 
and 0 otherwise, then the autocorrelation of such a temporal decay
is
The best fit between our data and the above-mentioned assumption leads to a 1.2-hour time scale of decay of turbulence.