2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/85507First, we make a revision of the up-to-date Passive Scalar Fields properties: also, the refractive index is among them. Afterwards, we formulated the properties that make the family of `isotropic' fractional Brownian motion (with parameter H) a good candidate to simulate the turbulent refractive index. Moreover, we obtained its fractal dimension which matches the estimated by Constantin for passive scalar, and thus the parameter H determines the state of the turbulence. Next, using a path integral velocity representation, with the Markovian model, to calculate the effects of the turbulence over a system of grids. Finally, with the tools of Stochastic Calculus for fractional Brownian motions we studied the ray-equation coming from the Geometric Optics in the turbulent case. Our analysis covers those cases where average temperature gradients are relevant.172 pages, 10 figures, PhD thesis (translated to English from the original Spanish version)OpticsAtmospheric and Oceanic PhysicsData Analysis, Statistics and ProbabilityFluid Dynamicstext