Geodesic
3D acoustic wave tracing in turbulent flows
Matematičeskoe modelirovanie, Tome 15 (2003) no. 7, pp. 75-80

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The present paper deals with digital acoustical ray tracing in 3D turbulent flows with a fluctuating acoustical index of refraction. The paths of the rays through the flow fields are computed from the ray equation in assumption of geometrical optics (short wavelengths). The refractive index field is prescribed on a $64\times64\times64$ grid using data from 3D direct numerical simulation of turbulence. The possibilities to reconstruct 3D correlation functions of the turbulence are analysed using 2D maps of the deflection angles of acoustic waves traces and a novel Erbeck–Merzkirch inverse integral transform. The last inversion is refered to ill-posed mathematical problems and some regularization techniques developed before for the Radon transform are applied. 
@article{MM_2003_15_7_a8,
     author = {N. A. Fomin and E. I. Lavinskaya and C. Greated},
     title = {3D acoustic wave tracing in turbulent flows},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {75--80},
     publisher = {mathdoc},
     volume = {15},
     number = {7},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2003_15_7_a8/}
}
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N. A. Fomin; E. I. Lavinskaya; C. Greated. 3D acoustic wave tracing in turbulent flows. Matematičeskoe modelirovanie, Tome 15 (2003) no. 7, pp. 75-80. http://geodesic.mathdoc.fr/item/MM_2003_15_7_a8/