Method for Measuring the Second-Order Moment of Atmospheric Turbulence

The turbulence moment of order m (μm) is defined as the refractive index structure constant Cn2 integrated over the whole path z with path-weighting function zm. Optical effects of atmospheric turbulence are directly related to turbulence moments. To evaluate the optical effects of atmospheric turbulence, it is necessary to measure the turbulence moment. It is well known that zero-order moments of turbulence (μ0) and five-thirds-order moments of turbulence (μ5/3), which correspond to the seeing and the isoplanatic angles, respectively, have been monitored as routine parameters in astronomical site testing. However, the direct measurement of second-order moments of turbulence (μ2) of the whole layer atmosphere has not been reported. Using a star as the light source, it has been found that μ2 can be measured through the covariance of the irradiance in two receiver apertures with suitable aperture size and aperture separation. Numerical results show that the theoretical error of this novel method is negligible in all the typical turbulence models. This method enabled us to monitor μ2 as a routine parameter in astronomical site testing, which is helpful to understand the characteristics of atmospheric turbulence better combined with μ0 and μ5/3.

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Large Aperture Laser Scintillometer for Measuring the Refractive Index Structure Constant of Atmospheric Turbulence

Chinese Journal of Lasers ◽

10.3788/cjl20083506.0898 ◽

2008 ◽

Vol 35 (6) ◽

pp. 898-902 ◽

Cited By ~ 1

Author(s):

马晓珊 Ma Xiaoshan ◽

朱文越 Zhu Wenyue ◽

饶瑞中 Rao Ruizhong

Keyword(s):

Refractive Index ◽

Atmospheric Turbulence ◽

Structure Constant ◽

Index Structure ◽

Large Aperture

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Second-order moment modeling of dispersed two-phase turbulence—Part 1: USM, k-ɛ-k p, and non-linear k-ɛ-k p two-phase turbulence models

Science China Physics Mechanics and Astronomy ◽

10.1007/s11433-011-4323-z ◽

2011 ◽

Vol 54 (6) ◽

pp. 1098-1107 ◽

Cited By ~ 5

Author(s):

LiXing Zhou

Keyword(s):

Turbulence Models ◽

Second Order ◽

Order Moment ◽

Two Phase ◽

Non Linear

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Experimental validation and design feasibility of a compact interferometric refractive index structure constant measurement sensor for atmospheric turbulence characterization

Laser Communication and Propagation through the Atmosphere and Oceans X ◽

10.1117/12.2594129 ◽

2021 ◽

Author(s):

Jay Land ◽

Daniel Whitley

Keyword(s):

Refractive Index ◽

Atmospheric Turbulence ◽

Experimental Validation ◽

Structure Constant ◽

Index Structure ◽

Measurement Sensor ◽

Constant Measurement

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Energy Spectra of Atmospheric Turbulence for Calculating Cn2 Parameter. I. Maidanak and Suffa Observatories in Uzbekistan

Atmosphere ◽

10.3390/atmos12121614 ◽

2021 ◽

Vol 12 (12) ◽

pp. 1614

Author(s):

Artem Yu. Shikhovtsev ◽

Pavel G. Kovadlo ◽

Evgeniy A. Kopylov ◽

Mansur A. Ibrahimov ◽

Shuhrat A. Ehgamberdiev ◽

...

Keyword(s):

Refractive Index ◽

Atmospheric Turbulence ◽

Baroclinic Instability ◽

Structure Constant ◽

Index Structure ◽

Energy Spectra ◽

Atmospheric Conditions ◽

Astronomical Observations ◽

Turbulence Spectra ◽

Wide Range

Knowledge of the turbulence spectra is of interest for describing atmospheric conditions as applied to astronomical observations. This article discusses the deformations of the turbulence spectra with heights in a wide range of scales at the sites of the Maidanak and Suffa observatories. It is shown that the energy of baroclinic instability is high at the sites of these observatories and should be taken into account in the calculations of the refractive index structure constant Cn2.

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Method of Estimation of Turbulence Integral Parameters

Applied Sciences ◽

10.3390/app11094157 ◽

2021 ◽

Vol 11 (9) ◽

pp. 4157

Author(s):

Hong Shen ◽

Longkun Yu ◽

Xu Jing ◽

Fengfu Tan

Keyword(s):

Refractive Index ◽

Linear Combination ◽

Adaptive Optics ◽

Structure Constant ◽

Index Structure ◽

Angle Of Arrival ◽

Weighting Functions ◽

Optical Effects ◽

Finite Distance ◽

Turbulence Parameters

The optical effects of turbulence are directly related to turbulence integral parameters, which are integrals of the refractive index structure constant over a whole path with different path-weighting functions (PWFs). We describe a method that utilizes measurable turbulence integral parameters, such as angle-of-arrival fluctuations and scintillation, to estimate turbulence integral parameters that cannot be measured directly. The estimates of the turbulence integral parameters are based on the linear combination of the PWFs of those measurable quantities. New measurable quantities and their PWFs under different propagation conditions were studied. Some interesting and meaningful results have been obtained. This method shows the prospect of characterizing anisoplanatism in adaptive optics and allows for the estimation of some optical turbulence parameters under non-ideal conditions, such as an isoplanatic angle in a finite distance.

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Nonlocal Convective PBL Model Based on New Third- and Fourth-Order Moments

Journal of the Atmospheric Sciences ◽

10.1175/jas3474.1 ◽

2005 ◽

Vol 62 (7) ◽

pp. 2189-2204 ◽

Cited By ~ 36

Author(s):

Y. Cheng ◽

V. M. Canuto ◽

A. M. Howard

Keyword(s):

Fourth Order ◽

Potential Temperature ◽

Turbulence Models ◽

Second Order ◽

Order Moment ◽

Third Order ◽

Mean Velocity ◽

Eddy Simulation ◽

Analytic Expressions ◽

Aircraft Data

Abstract The standard approach to studying the planetary boundary layer (PBL) via turbulence models begins with the first-moment equations for temperature, moisture, and mean velocity. These equations entail second-order moments that are solutions of dynamic equations, which in turn entail third-order moments, and so on. How and where to terminate (close) the moments equations has not been a generally agreed upon procedure and a variety of models differ precisely in the way they terminate the sequence. This can be viewed as a bottom-up approach. In this paper, a top-down procedure is suggested, worked out, and justified, in which a new closure model is proposed for the fourth-order moments (FOMs). The key reason for this consideration is the availability of new aircraft data that provide for the first time the z profile of several FOMs. The new FOM expressions have nonzero cumulants that the model relates to the z integrals of the third-order moments (TOMs), giving rise to a nonlocal model for the FOMs. The new FOM model is based on an analysis of the TOM equations with the aid of large-eddy simulation (LES) data, and is verified by comparison with the aircraft data. Use of the new FOMs in the equations for the TOMs yields a new TOM model, in which the TOMs are damped more realistically than in previous models. Surprisingly, the new FOMs with nonzero cumulants simplify, rather than complicate, the TOM model as compared with the quasi-normal (QN) approximation, since the resulting analytic expressions for the TOMs are considerably simpler than those of previous models and are free of algebraic singularities. The new TOMs are employed in a second-order moment (SOM) model, a numerical simulation of a convective PBL is run, and the resulting mean potential temperature T, the SOMs, and the TOMs are compared with several LES data. As a final consistency check, T, SOMs, and TOMs are substituted from the PBL run back into the FOMs, which are again compared with the aircraft data.

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