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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. gif 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. gif):

  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.
The temperature fluctuations are largest at the base of the wall layer and strongly intermittent as they are caused by the plumes of fluid coming from the top of the conductive layer. The intermittency of these temperature fluctuations is in particular driven by the velocity fluctuations in the upper layer, which in turn depend on the form and general characteristics of the whole convective cell.

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 (gif) derived by Wyndham on the basis of measurements in the atmospheric surface layer, that is at a much larger geometric scale.

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

next up previous contents
Next: Mixed and forced Up: Physical description of Previous: Physical description of

Lorenzo Zago,, Sun Feb 26 22:57:31 GMT+0100 1995