We have simulated optical propagation through atmospheric turbulence in which the spectrum near the inner scale follows that of Hill and Clifford [J. Opt. Soc. Am. 68, 892 (1978)] and the turbulence strength puts the propagation into the asymptotic strong-fluctuation regime. Analytic predictions for this regime have the form of power laws as a function of β_(0)~(2), the irradiance variance predicted by weak-fluctuation (Rytov) theory, and l_(0), the inner scale. The simulations indeed show power laws for both spherical-wave and plane-wave initial conditions, but the power-law indices are dramatically different from the analytic predictions. Let σ_(I)~(2)-1=α(β_(0)~(2)/β_(c)~(2))~(-b)(l_(0)/R_(f))~(c), where we take the reference value of β_(0)~(2) to be β_(c)~(2)=60.6, because this is the center of our simulation region. For zero inner scale (for which c=0), the analytic prediction is b=0.4 and a=0.17 (0.37) for a plane (spherical) wave. Our simulations for a plane wave give a=0.234±0.007 and b=0.50±0.07, and for a spherical wave they give a=0.58±0.01 and b=0.65±0.05. For finite inner scale the analytic prediction is b=1/6, c=7/18 and a=0.76 (2.07) for a plane (spherical) wave. We find that to a reasonable approximation the behavior with β_(0)~(2) and l_(0) indeed factorizes as predicted, and each part behaves like a power law. However, our simulations for a plane wave give a=0.57±0.03, b=0.33±0.03, and c=0.45±0.06. For spherical waves we find a=3.3±0.3, b=0.45±0.05, and c=0.8±0.1.
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