Scintillations due to a concentrated layer with a power-law turbulence spectrum


  • V. H. Rumsey


The spatial spectrum of intensity fluctuations due to a concentrated layer of turbulence is derived from the parabolic wave equation. The spectrum of refractive index fluctuations is taken to be an unmodified power law of arbitrary strength, with exponent α, 2 < α < 6. For 2 < α < 4 it is shown that the intensity spectra for a plane wave can be expressed in terms of a single parameter U, which is the Born approximation to m2, the normalized variance of intensity fluctuation. For U ≪ 1 the Born approximation applies. The high frequency approximation to the intensity spectrum is the angular spectrum that would result from twice the strength of turbulence. It applies above the spatial frequency κf or 2π κf/U, whichever is smaller, where κf is the frequency at the first null of the Born approximation. For U > 30, it represents essentially all of the intensity fluctuations and shows that m saturates at unity for a plane wave as U → ∞. Simple formulas for m when the source has finite angular extent show that m decreases with increasing turbulence as Uα−2 for U ≫ 1. These results are confirmed by exact calculations for the case α = 3 and by extensive observations of interplanetary scintillations.