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Interaction between a turbulent plasma flow like solar o stellar wind and a magnetic field as an obstacle is very common for space and astrophysical plasmas. The magnetosphere of the Earth is formed precisely as a result of such interaction, and there is a vast amount of evidence suggesting that the geomagnetic tail is like a turbulent wake behind an obstacle. These solar wind turbulent fluctuations are strongly amplified after crossing the bow shock,forming the plasma flows in the magnetosheath. At the same time, the geomagnetic tail contains the plasma sheet filled by dense and turbulent plasmas and tail lobes filled by a rare quasi-laminar plasmas. The Large-scale vortices in the wake are able to generate turbulent transport that takes place both along the plasma sheet, in the X and Y directions, and across the plasma sheet, in the Z direction. Thus, turbulent fluctuations in all directions should be taken into consideration when analyzing plasma transport in the plasma sheet, and stability of the plasma sheet itself. The interaction between the turbulent plasma sheet and the inner magnetosphere regions is important for understanding of the key magnetospheric processes such as geomagnetic storms and substorms. At the same time, the variations in the solar wind density, velocity, and interplanetary magnetic field consonantly change the plasma conditions both in the plasma sheet and the inner magnetosphere, but due to different and not fully understood mechanisms. Data from CLUSTER, and Themis satellites are used to analyse the stability of turbulent plasma sheet and turbulent transport for different solar wind conditions and geomagnetic activity.The results obtained show that the level of turbulence in the plasma sheet, characterized by the eddy diffusion, correlates with the dawn-dusk electric field, and depends of the solar wind and IMF parameters for both quiet and disturbed geomagnetic conditions.