If a forced flow interacts with buoyancy forces the wall
region and, in part, the conductive layer
will be destabilized by the velocity gradients.
In the turbulent region (see fig. ) the turbulent
diffusivity will increase rapidly with the distance from the surface,
with a consequent reduction of the temperature fluctuations.
The profile of
above the surface will be such
that the maximum is at the interface
between the viscous-conductive layer and the overlying turbulent layer
but will decrease more rapidly than in the free convection case.
Figure: Temperature and velocity fluctuations in presence of
forced flow over a horizontal plane
All the experimental and anecdotal evidence shows that very little
seeing will be produced if a forced convection regime is fully
established as in that case the viscous-conductive layer becomes very
thin and the temperature turbulence profile decreases very rapidly.
A more significant case is the intermediate situation in which a weak
air flow interacts with free convection producing a mixed convection
regime. This will be characterized by the Froude ()
and Reynolds (
) numbers.
When the Froude number is large, forced convection is dominant and
therefore
mirror seeing should disappear. When the Froude number is small, free
convection is dominant.
The amplitude of the temperature turbulence profile is
determined by the turbulent eddy diffusivity so that for our purpose
the turbulence regime similarity is defined by the turbulent Reynolds
number, proportional to the turbulence intensity -
see ():
Therefore in the mixed convection case,
identity of the Froude number and turbulence intensity
is required for any similarity between tests at different scales.
In section we will show that the rate of seeing
produced by a given mirror-air temperature difference is indeed a
function of the Froude number.