Shell models of turbulence were used to study the effect of isotropic turbulence on the refractive index spectrum for the case of a plane wave beam propagation through turbulent flow. Existing theories of the 1D and 3D temperature spectra was shown to be inaccurate in the dissipative range of the spectrum due to unresolved scales at high Reynolds numbers. The shell model explaining the buoyancy driven turbulence was chosen as a tool to consider density changes with temperature and resolve all the range of wavenumbers up to the Kolmogorov's scale. The physical nature of the Hill bump (increase of the slope of the energy spectrum), observed in the transition region between inertial-convective and viscous-diffusive parts of the cascade was explored. It was shown, that no Hill bump is formed if the sufficient number of shells is chosen to resolve all spectrum, but the Hill bump will appear at the additional non-compensated forcing at large wavenumbers. The calculated shell-averaged temperature spectrum was used to determine the refractive index power spectral density and to create 2D phase-screens for modeling the laser beam propagation in the formed turbulent flow. Verification and validation of the combined shell model aero-optics problem was done by the comparison of the irradiance profiles with the laboratory experimental data and Direct Numerical Simulations for the case of a 532 nm laser beam propagation in grid generated turbulence and for the case of the buoyancy driven turbulence. The turbulent velocity and temperature spectrum generated by the shell model was shown to be comparable to the Modified Von-Karman theory. Good quantitative agreement with the experimental data confirmed that the main source of the laser beam distortion at considered conditions relates to the thermal distortions.
