Magnetosheath is a transition layer between the solar wind and the magnetosphere and may contribute to the geoeffectiveness of various large-scale interplanetary phenomena. In this paper, we examine the dynamics of the turbulent fluctuation spectra behind the bow shock during undisturbed solar wind and when interplanetary coronal mass ejections and corotation interaction regions interact with the magnetosphere. The study is based on statistical analysis of the turbulence features inside the magnetosheath at different distances from the bow shock. We demonstrate that the turbulence features change when plasma crosses the bow shock for the solar wind of all types and they usually recover when plasma moves away from the bow shock. However, peculiarities in the turbulence development occur during interplanetary coronal mass ejections. Moreover, during disturbed solar wind there are relations between the turbulence features at the sub-ion scales and background plasma parameters such as plasma parameter β, the angle θBN between the interplanetary magnetic field and the local bow shock normal, solar wind bulk velocity, and the distance to the magnetosheath boundaries.