[en] Full text: Direct quantitative validation of gyro-kinetic nonlinear simulations has been successfully achieved versus turbulence measurements on Tore Supra L-mode plasmas. Local density fluctuations measurements have been performed with Doppler and fast-sweeping reflectometry. The nonlinear simulations are performed using the Eulerian code GYRO and the semi-Lagrangian GYSELA retaining different physical effects, namely adiabatic/kinetic electrons, local/global approach, collisions, electromagnetic and finite aspect ratio effects. For the first time, the numerical local results simultaneously match within experimental uncertainty not only the high-order scalar observables, as the radial profiles of the effective heat diffusivity and rms values of density fluctuations δn/n, but coherently, also the related spectral quantities, namely the wave-number δn/n power spectra along both the perpendicular k_θ and k_r perpendicular vectors. At the same radial position, dissimilar power spectral exponents in the transverse plane are found by the measurements, respectively α_θ=-4.3±0.7 and α_r=-2.7±0.25 at scales corresponding to 0.4< k_{perpendicular}ρ_s<1.0: this could initially suggest a highly anisotropic turbulence favouring the formation of radially elongated structures. However, when the differences in instrumental responses are properly taken into account in the light of nonlinear simulations, the experimental anisotropy, which is clearly present around k_{perpendicular}ρ_s∼0.2, was found to be partly due to instrumental effects, with a remaining, weaker physical anisotropy. (author)