Seeing computation by means of a fluid flow numerical model

We recall that the seeing FWHM angle is an integral function of the temperature structure coefficient which in turn can be defined in terms of the two dissipation quantities (momentum) and (temperature) - see equation () at page . If a k- scheme is used in the model the dissipation rate and the eddy diffusivities and are readily available in the program output. One can then compute numerically the temperature dissipation at any node by computing numerically its definition over the model grid:

Thus can be evaluated at each node of the model and integrated according to () to obtain the FWHM angle. This general procedure is summarized in fig. below.

  
Figure: General procedure for evaluating seeing from a CFD model

One such model has been developed under an ESO contract by the Risø National Laboratory (Denmark) with the purpose of computing theoretical seeing profile through the atmospheric surface layer in mountain terrain [de Baas]. The outcome of this work outlined some problems associated with the use of CFD models for seeing evaluation:

• In order to give reliable results, a CFD model should well represent all significant characteristics of the solid-fluid interface, from friction effects to shear flow and heat transfer. However, the structures surrounding a telescope are generally very complex, which makes the development of a model grid a long effort and adds greatly to its size.
• The conditions, both aerodynamic and thermal of the local atmospheric environment are often not known with the detail and extent that would be required for an accurate and comprehensive model. Also those conditions are very variable, which also adds to the effort involved and makes experimental verifications objectively difficult.

More recently a simulation aiming at predicting seeing through the entire atmosphere was attempted at Meteo-France by means of the mesoscale numerical weather prediction model PERIDOT [Bourgeault]. The model was quite comprehensive in incorporating accurate representations of radiative and friction transfer and of turbulence in general, being used operatively for meteorologic predictions. A favorable comparisons of model output and seeing measurements is reported, although some reserves on the effective usefulness of the results were expressed because the model low resolution (respectively 10 km and 3 km in the two cases studied).