Single Taylor screen model

One of the simplest temporally varying models for the atmosphere is that of a single Taylor screen moving at a constant wind velocity. The simplicity of this model has made it appealing to a number of previous authors. Roddier et al. (1982a); Lopez & Sarazin (1993) note that for speckle imaging at large apertures this model can provide quite different temporal characteristics to models with multiple Taylor screens having a scatter of different wind velocities. For this reason I will introduce a simplified model for a single wind-blown Taylor screen atmosphere which will help in highlighting the unusual properties of these atmospheres.

As discussed above and in Aime et al. (1986); Roddier et al. (1982a), if the scatter $\Delta v$ is small the timescale for changes in the image plane will be related to the wind crossing time of the telescope aperture. This will certainly apply for the case of a single Taylor screen atmosphere as in this case $\Delta v$ is zero. A demonstration of this relationship is given for a simplified approximation to a single Taylor screen atmosphere in Appendix A. The timescale $\tau _{e}$ for changes to the speckle pattern in a telescope aperture of diameter $d$ for this simplified model is found to be:

$$\tau_{e}=\frac{0.31d}{\left \vert \mathbf{v} \right \vert}$$ (2.13)

for a constant wind velocity $\mathbf{v}$ (Equation A.16).

It is interesting to note that $\tau _{e}$ is independent of the atmospheric coherence length $r_{0}$ with the simple model used for a single layer of atmospheric turbulence.