Measurement of energy distributions in the wave vector domain reveals how anisotropy of turbulent magnetic field fluctuations evolves as the solar wind encounters the terrestrial bow shock and the magnetosphere. While fluctuations in the solar wind, the magnetosheath, and the magnetospheric cusp regions are characterized by the perpendicular wave vector geometry to the mean magnetic field direction, that in the foreshock region is characterized by the parallel wave vector geometry. Linear and nonlinear plasma processes are discussed for the anisotropy evolution. Key words: Wave-vector spectra, magnetic field, bow shock, multi-point measurements.Many in-situ spacecraft observations suggest that shock waves in the interplanetary space such as planetary bow shocks and traveling shocks in the co-rotating interaction regions are often accompanied by turbulent fluctuations, and furthermore, there are indications that interstellar shocks or supernova remnants may be associated with turbulence (Hester et al., 1994;Spitler and Spangler, 2005). How turbulence evolves as it encounters the shock wave in a collisionless plasma is an interesting problem and of particular importance in space physics and astrophysics. Earth's bow shock, a standing shock wave located at about 20 Earth radii in front of the Earth, serves as an ideal, natural laboratory for studying turbulence evolution across the shock. Many spacecraft visited the Earth's bow shock and observed various kinds of electrostatic and electromagnetic fluctuations near the shock, e.g., Shin et al. (2007). Spatial properties of waves or turbulence in the surroundings of the bow shock can be extensively studied by the Cluster mission (Escoubet et al., 2001), as it provides four-point measurements in the near-Earth space.Here we present a measurement of energy distributions of magnetic field fluctuations in the wave vector domain using the Cluster fluxgate magnetometer data . We use the concept of two distinct fluctuation geometries to study anisotropy: parallel and perpendicular wave vector geometries (Fig. 1). The idea of the two fluctuation geometries is motivated by long-standing questions about the nature of symmetries of plasma turbulence, viz., whether wave vectors in plasma turbulence prefer parallel or perpendicular directions to the mean magnetic field (Matthaeus et al., 1990;Carbone et al., 1995).We investigate the magnetic field data for two Cluster orCopy right