Based on the extended Huygens-Fresnel (eHF) principle, approximate analytical expressions for the spectral density of nonuniformly correlated (NUC) beams are derived with the help of discrete model decompositions. The beams are propagating along horizontal paths through an anisotropic turbulent medium. Based on the derived formula, the influence of the anisotropic turbulence (anisotropy factors, structure parameters) on the evolution of the average intensity, the shift of the intensity maxima and the power-in-the-bucket (PIB) are investigated in detail through numerical examples. It is found that the lateral shifting of the intensity maxima is closely related to the anisotropy factors and the strength of turbulence. Our results also reveal that, in the case of weak turbulence, the beam profile can retain the feature of local intensity sharpness, but this feature degenerates quickly if the strength of the turbulence increases. The value of PIB of the NUC beams can be even higher than that of Gaussian beams by appropriately controlling the coherence parameter in the weak turbulence regime. This feature makes the NUC beams useful for free-space communication.