Free convection

Free convection at a plate surface develops typically through large convective cells the regime of which is characterized by the Raleigh number:

At low Raleigh numbers the flow is laminar, although it may be unstable, until a transition at to a fully turbulent regime.

Recalling that telescope enclosures will typically have during night-time a stable stratification due to the daytime interior air cooling, even where the floor is not deliberately chilled, we may find some analogy with studies relative to the urban "heat island" problem which is also characterized by an ambient stable stratification. Experiments reported by [Hertig 86] and [Giovannoni] have shown that for a large single surface and particularly in presence of an ambient stable stratification the convective cell can become unstable already at and form a turbulent central nucleus if the length

is greater than m.

Fig. from [Hertig 86] illustrates the different regimes found experimentally for a convective cell with an ambient stable stratification. The height of the cell will depend theoretically on the stratification of ambient air. In a free neutral medium the plume would simply ascend until its energy is exhausted (free plume).

  
Figure: Convection regimes as a function of Ra and

  
Figure: Temperature and velocity fluctuations in free convection over a horizontal plane

Since the temperature fluctuations are greater very close to the surface-air interface, that is the region where we would expect that the mirror seeing effect is generated. Looking more in detail at the mechanism of free convection heat transfer from a horizontal plane, one distinguishes three regions (fig. ):

1. A viscous-conductive layer in which heat is transferred by molecular conduction. The thickness of this layer may be estimated equal to the free convection wall scale [Townsend]:

    

2. A wall region characterized by the emergence of rising plumes of warm fluid (and falling plumes of cold fluid) in which the mean temperature gradients, hence the temperature fluctuation intensity, are largest.
3. A farther region in which mean velocities and velocity fluctuations are largest but temperature gradients are negligible.

Therefore most of the mirror seeing is generated in a thin region just above the viscous-conductive layer, itself quite thin (in the range of millimeters) where the temperature fluctuations are largest. If it could be visualized, seeing would appear almost "floating" above the surface. This fact suggests that the mean value of mirror seeing, as it takes its origin so close to the surface, should predominantly be a function of the surface flux and could also be described by the expression () derived by Wyndham on the basis of measurements in the atmospheric surface layer, that is at a much larger geometric scale.

In section we will indeed verify the hypothesis that equation () is valid to a good approximation also for the mirror seeing scale down to the height of the conduction layer (see fig. ).