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- W2036534315 abstract "AbstractThe definition of the inner scale for atmospheric turbulence is given. Methods of meas uring inner scale are discussed and typical values are given. Inner-scale effects on irra diance covariance and log-amplitude covariance are discussed for both weak and strong scin tillation. The covariance width is limited by the inner scale for saturated scintillation.What is the inner scale?The inner scale was first defined in terms of the temperature structure function DT(r) by Obukhov.1 He defined the inner scale £ to be that spacing r at which the inertia! range form of the temperature structure function equals its dissipation range form.DT(r) E (1)= CT2 r2^ in inertial range (2)= (x/6D)r2 = in diffusive dissipation range (3)where angle brackets denote an average, CT2 is the temperature structure parameter, D is the diffusion coefficient of heat in air, and x is the rate of diffusive dissipation of mean-squared temperature fluctuations. Thus, £ is defined byV ^o^ = /D)~3/4 n = 7.4 n (7)The coefficients in Eqs . (5) and (7) are uncertain by roughly 10% because of uncertainties in the value of the Obukhov-Corrsin constant;4 thus one finds different values of these coefficients in the literature. The relationships (1) through (7) are described in Tatarskii's tome,5 although his notation is different than that used here.Other so-called inner scales have been used for optical propagation. For instance, Strohbehn6 calls £ the inner scale where the dissipation range of the temperature spec trum is modeled by°multiplying the inertial range form by exp[-K2/(27t/je ) 2] . Tatarskii5 shows that the factor is exp [-K2/(5.92/£ ) 2 ] with £ from Eq. (4). Thuiy A = 1.06 £ . Furthermore, every structure function has its own inner scale. For instance, the humiaity structure function has an inner scale slightly different from that of the temperature structure function because the diffusion coefficient of water molecules in air is about 14% larger than that of heat in air, and Eq. (5) then gives a larger inner scale. The struc ture function arising from the temperature-humidity correlation has an intermediate inner scale because its effective diffusion coefficient is the average of those of humidity and heat. In this paper the refractive-index inner scale is taken to be the same as for tem perature. The implications for the refractive-index spectrum of these differing tempera ture and humidity inner scales is illustrated in Ref. 7.Propagation structure functions have their own inner scales. For instance, the wave structure function changes from r5^ at inertial range scales to r2 at dissipation range67" @default.
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- W2036534315 date "1983-07-12" @default.
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- W2036534315 title "<title>Inner-Scale Effect On The Irradiance Of Light Propagating In Atmospheric Turbulence</title>" @default.
- W2036534315 doi "https://doi.org/10.1117/12.935756" @default.
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