Regimes of optical propagation through turbulence: theory and direct numerical simulations

Classical work provides an analytical framework to predict distortions of an electromagnetic wave as it interacts with turbulence. However, there seems to be virtually no systematic validation of these predictions and assessment of the assumptions behind the theory. In this work, we present numerical results of optical distortions based on highly-resolved direct numerical simulations of turbulence at a range of conditions, and new theory which accounts for more realistic representations of turbulent fluctuations. This leads to a number of new results. First, we discover two new scaling regimes for the variance of phase and log-amplitude at propagations comparable to Kolmogorov scales. Second, our theory highlights and overcomes limitations of classical work including the effects of finite outer-scale, non-Kolmogorov intermittency corrections, and a more general representation of small scales. Third, we propose a new universal refractive-index structure parameter in terms of three non-dimensional parameters involving turbulence and optical scales. This yields a universal presentation of all scaling regimes in a new phase space. Finally, high-fidelity direct numerical simulations which resolve all turbulent scales are used to perform the first systematic assessment of classical and new scaling regimes. Excellent agreement is found between simulations and theoretical findings.