We study the structure and properties of the lunar wake with these solar wind parameters: the angle $theta$sw between directions of the solar wind velocity vsw and the ambient interplanetary magnetic field (IMF) B $theta$sw = 45¿ and 90¿ and vsw = 6vA (where vA denotes solar wind Alfv¿n velocity). We examine the structure of the wake-tail formed behind the obstacle. In agreement with in situ observations the lunar wake is formed by two counterstreaming beams which fill the wake with a relatively cold, inhomogeneous and highly anisotropic plasma. The results of this study suggest that for given solar wind conditions the downstream region of the lunar wake is dominated by electromagnetic turbulence with the frequencies near the local proton gyrofrequency. The properties and possible generating mechanisms of the low-frequency electromagnetic turbulence are discussed.