Modelling of turbulence induced quasi-static aberrations at extremely large telescope scales

ABSTRACT A simulation has been used to explore the decay rates of time-averaged atmospheric turbulence residuals under frozen flow conditions. We have used our model to show that there is a significant variation in the power-law exponent when individual Zernike modes within the same azimuthal pair are considered. We have shown via simulation that the characteristic time-scale needed for a time-averaged Zernike mode to achieve a specified residual wavefront variance is dependent upon wind direction, meaning that both the $C_{n}^{2}$ and wind velocity profiles can have a large effect on the modal variance of observed quasi-static aberrations. Results are presented for both a single layer atmospheric model and an ESO standard 35 layer model – with wind directions and ground layer speeds taken from on-sky data. We model a 39 m telescope, demonstrating that for low order modes averaging to a threshold of $\lambda /20$ at 550 nm may take thousands of seconds, which is substantially longer than the typical update rates of telescope control systems.