** Discussion of experimental data**

We have seen that mirror seeing due to pure free convection should be proportional to with an exponent ranging from 1 to 1.3 . We will consider here as a baseline a proportionality to . Examination of the experimental measurements leads to the following conclusions:

- The data from the CFHT telescope, analyzed in section and appendix indicate a proportionality factor of 0.38 arcsec/K.
- In the Japanese 62-cm mirror experiment the factor to lies between 0.25 and 0.34, although in fact the data would be better fitted with an exponent greater than 1.2.
- For the 254-mm experiment of Lowne the factor to lies between 0.28 (for = 8K) and 0.45 (for = 2K). The exponent would appear here to be lower than 1.
- The experimental measurements of the author with a 4-cm mirror indicate for s up to 22K factors between 0.25 and 0.54.

The discrepancies between the various experiments must not surprise as the measurement methods, the experiment set-ups, the range of temperatures explored and the environmental conditions differed greatly. Nevertheless the basic concordance of data over the large range of mirror diameters and other conditions provides some useful indications:

- Mirror seeing in free convection conditions appears approximately independent of mirror size.
- As the range of experimental conditions must have covered many different flow regimes (cf. fig. ) it appears that that mirror seeing is a quite "robust" phenomenon as its quantification does not depend exceedingly on the particular conditions of the flow regime.
- As seeing appears already in small mirrors with low s, associated with very low Raleigh numbers, it must be concluded that also fluctuations and instabilities in laminar flow regimes do produce seeing whose magnitude is of the same order as in fully turbulent regimes.

Emphasizing the weight to the CFHT data, we will here propose the following relationship for the purpose of engineering parametric studies:

One should make allowance for possible variations of the order to
25%.

Fig. shows the reasonable agreement of
equation () with respect to all the laboratory data.

\

** Similarity theory model**

In section we have illustrated how the production of mirror seeing takes place very close to the surface, in the region near the interface between the viscous conductive layer and the emerging plumes of warmer air. It follows that the phenomenon depends essentially only on one, namely vertical, geometrical coordinate. The hypothesis was expressed that the profile of the temperature structure coefficient above the viscous conductive layer over a mirror should follow the same similarity law () as in the atmospheric surface layer, in spite of the large difference of geometric scale.

The maximum value of will be found at the top of the viscous conductive layer, the thickness of which is computed by the expression from [Townsend] as:

is zero at the surface and will be linearly interpolated in the viscous conductive layer. Thus the vertical profile of is described by

The seeing FWHM angle is then obtained by integrating equation
() * twice*
over the height significant for seeing effects:

where is given by equation ():

obtaining:

This model has been used to simulate the different laboratory experiments described above. In these simulations, the surface flux was computed by the textbook relationship between the Nusselt and Raleigh numbers for the laminar regime ():

A computed profile of is shown in fig. . One may note that in this typical example (mirror diameter 62-cm, mirror-air = 1K) the near totality of mirror seeing is produced in the first 2 cm above the mirror surface.

The integral seeing values resulting from the simulations are plotted in fig. over the experimental data. The good agreement indicates that a similarity model described by equations (5.40-42) does account well for the observed seeing effects.

Lorenzo Zago, zago@elgc.epfl.ch, Sun Feb 26 22:57:31 GMT+0100 1995