On the wavelength dependence of the effects of turbulence on average refraction angles in occultations by planetary atmospheres

Abstract

Two recent adjacently published papers on the average effects of turbulence in radio and optical occultation studies of planetary atmospheres appear to disagree on the question of wavelength dependence. It is demonstrated here that in deriving a necessary condition for the applicability of their method. Hubbard and Jokipii neglect a factor which is proportional to the square of the ratio of the atmospheric or local Fresnel zone radius and the inner scale of turbulence. They also fail to establish sufficient conditions, thereby omitting as a further factor the square of the ratio of atmospheric scale height and the local Fresnel zone radius. The total descrepancy, which numerically is typically within several orders of magnitude of 10/sup 11/ for radio and 10/sup 7/ for optical occultations, means that their results correspond to geometrical optics and not to wave optics as claimed. Thus their results are inherently inapplicable in a discussion of the wavelength dependence of any parameter, such as the bias in the average refraction angle treated by Eshleman and Haugstad. We note that for power spectra characterized by the (--p) exponent of the turbulence wavenumber, the average turbulence-induced bias in refraction angles depends on the radiation wavelength as lambda/sup( p/--4)/2,more » or as lambda/sup en-dash1/6/ for Kolmogorov turbulence. Other features of the Hubbard-Jokipii analysis are also discussed.« less