Free convection at a plate surface develops typically through large
convective cells the regime of which is characterized by the three
dimensionless numbers Fr, Re, Pr (see page ).
The Froude number characterizes the buoyancy force but is
inconvenient in its present form, because it is
expressed in terms of a reference velocity U which is not clearly
defined. It is therefore customary to work with the
Raleigh number:
At low Raleigh numbers the flow is deemed 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, here is 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. ):
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
Wyngaard for 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.
).