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Adaptive Optics in the VLT and ELT era Atmospheric Turbulence François Wildi Observatoire de Genève Credit for most slides : Claire Max (UC Santa Cruz) Page 1 Atmospheric Turbulence Main Points • We, in astronomy, are essentially interested in the effect of the turbulence on the images that we take from the sky. This effect is to mix air masses of different index of refraction in a random fashion • The dominant locations for index of refraction fluctuations that affect astronomers are the atmospheric boundary layer and the tropopause • Atmospheric turbulence (mostly) obeys Kolmogorov statistics • Kolmogorov turbulence is derived from dimensional analysis (heat flux in = heat flux in turbulence) • Structure functions derived from Kolmogorov turbulence are r2/3 Fluctuations in index of refraction are due to temperature fluctuations • Refractivity of air 3 P 7.52 10 6 N (n 1) 10 77.6 1 2 T where P = pressure in millibars, T = temp. in K, in microns n = index of refraction. Note VERY weak dependence on • Temperature fluctuations index fluctuations N 77.6 (P / T )T 2 (pressure is constant, because velocities are highly sub-sonic. Pressure differences are rapidly smoothed out by sound wave propagation) Turbulence arises in several places stratosphere tropopause 10-12 km wind flow around dome boundary layer ~ 1 km Heat sources w/in dome Within dome: “mirror seeing” • When a mirror is warmer than dome air, convective equilibrium is reached. credit: M. Sarazin • Remedies: Cool mirror itself, or blow air over it, improve mount credit: M. Sarazin convective cells are bad To control mirror temperature: dome air conditioning (day), blow air on back (night) Local “Seeing” Flow pattern around a telescope dome Cartoon (M. Sarazin): wind is from left, strongest turbulence on right side of dome Computational fluid dynamics simulation (D. de Young) reproduces features of cartoon Boundary layers: day and night • Wind speed must be zero at ground, must equal vwind several hundred meters up (in the “free” atmosphere) • Boundary layer is where the adjustment takes place, where the atmosphere feels strong influence of surface • Quite different between day and night – Daytime: boundary layer is thick (up to a km), dominated by convective plumes – Night-time: boundary layer collapses to a few hundred meters, is stably stratified. Perturbed if winds are high. • Night-time: Less total turbulence, but still the single largest contribution to “seeing” Real shear generated turbulence (aka KelvinHelmholtz instability) measured by radar • Colors show intensity of radar return signal. • Radio waves are backscattered by the turbulence. Kolmogorov turbulence, cartoon solar Outer scale L0 Inner scale l0 h Wind shear convection h ground Kolmogorov turbulence, in words • Assume energy is added to system at largest scales “outer scale” L0 • Then energy cascades from larger to smaller scales (turbulent eddies “break down” into smaller and smaller structures). • Size scales where this takes place: “Inertial range”. • Finally, eddy size becomes so small that it is subject to dissipation from viscosity. “Inner scale” l0 • L0 ranges from 10’s to 100’s of meters; l0 is a few mm Assumptions of Kolmogorov turbulence theory • Medium is incompressible • External energy is input on largest scales (only), dissipated on smallest scales (only) – Smooth cascade • Valid only in inertial range L0 • Turbulence is – Homogeneous – Isotropic Questionable at best • In practice, Kolmogorov model works surprisingly well! Concept Question • What do you think really determines the outer scale in the boundary layer? At the tropopause? • Hints: Outer Scale ~ 15 - 30 m, from Generalized Seeing Monitor measurements • F. Martin et al. , Astron. Astrophys. Supp. v.144, p.39, June 2000 • http://www-astro.unice.fr/GSM/Missions.html Atmospheric structure functions A structure function is measure of intensity of fluctuations of a random variable f (t) over a scale t : Df(t) = < [ f (t + t) - f ( t) ]2 > With the assumption that temperature fluctuations are carried around passively by the velocity field (for incompressible fluids), T and N have structure functions like • • DT ( r ) = < [ T (x ) - v ( T + r ) ]2 > = CT2 r 2/3 DN ( r ) = < [ N (x ) - N ( x + r ) ]2 > = CN2 r 2/3 Typical values of CN2 • Index of refraction structure function DN ( r ) = < [ N (x ) - N ( x + r ) ]2 > = CN2 r 2/3 • Night-time boundary layer: CN2 ~ 10-13 - 10-15 m-2/3 10-14 Paranal, Chile, VLT Turbulence profiles from SCIDAR Eight minute time period (C. Dainty, Imperial College) Siding Spring, Australia Starfire Optical Range, Albuquerque NM Atmospheric Turbulence: Main Points • The dominant locations for index of refraction fluctuations that affect astronomers are the atmospheric boundary layer and the tropopause • Atmospheric turbulence (mostly) obeys Kolmogorov statistics • Kolmogorov turbulence is derived from dimensional analysis (heat flux in = heat flux in turbulence) • Structure functions derived from Kolmogorov turbulence are r2/3 • All else will follow from these points!