Outer scale of turbulence appropriate to modeling refractive-index structure profiles

Abstract

The outer scale of turbulence L (0) has been calculated from values of the refractive-index structure coefficient C(2)(N) obtained from spatio-angular correlation measurements of stellar scintillation. It is found that L(0) </= 5 m for a large range of observations in France, U.S.A., and Chile and that its dependence on altitude Z follows the same general form at all these sites. The prediction of C(2)(N)(Z) profiles is shown to be feasible utilizing standard meteorological radiosonde data and this L(0)(Z) curve. A simple model based on dimensional analysis and a more complicated stochastic model are compared, but the latter appears to have no advantage.

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“…But as pointed out by Coulman et al (1988) Coulman et al (1986), using a model developed by André et al (1978), have shown that, even if the results were not as good as expected, the model Masciadri et al (2001) considering the temperature near the ground and around the telescope at the Roque de Los Muchachos Observatory. The simulations are close to the measurements, with a comparable dispersion, but the physical time for the model to reach a thermodynamic and kinetic equilibrium is at least 3 hr.…”

“…Models derived from the Tatarski formula give profiles 2 C N from meteorological data. According to Coulman et al (1988), it should be possible to deduce the profile from the ). The temperature T in K, the pressure P in hPa, and the mean potential temperature 2 v in K are function of the altitude h in m. Tatarski's formula is derived from the study of the microstructure of the concentration of conservative and passive additives in a turbulent flow.…”

“…First, Coulman et al (1988) Abahamid et al (2004a), and extended toward the boundary layer (eq. [6]).…”

Online estimation of the wavefront outer scale profile from adaptive optics telemetry

“…This means that the use of a single L 0 is not adequate to describe the spatial coherence of the atmosphere, since the response function can be the result of combining slopes from more than one layer, each with different outer scale values, i.e. a profile or L 0 (h) (Coulman et al 1988;Lukin, Fortes & Nosov 1998;Dali et al 2010;Ziad et al 2013). …”

Towards the monitoring of atmospheric turbulence model

“…These models are empirical and up to now nothing could decide in favour of one of them. In addition, the small values found for the outer scale (Coulman et al 1988) reduce significantly the inertial range and therefore the Kolmogorov model field to take into account the turbulence effects in the performance of large telescopes and long baseline interferometers.…”