The Cluster satellites crossed the Earth's bow shock several times on 31 March 2001. For all these crossings the bow shock was supercritical and quasi-perpendicular. We present here the results of a detailed analysis of the magnetic field fluctuations observed downstream of the shock. We use data from the four Cluster spacecraft to determine the behavior and the geometry of these fluctuations with good accuracy. Shortly after the ramp crossing, we observed a large-amplitude nonlinear Alfvén wave, propagating along the downstream average magnetic field with a spectrum peaking at two frequencies below the proton and the alpha ion cyclotron frequencies. Farther downstream in the magnetosheath the magnetic field fluctuations took the form of three-dimensional structures which can be interpreted as cylindrical field-aligned current tubes. It is the first time that such current tubes have been observed downstream of a quasi-perpendicular shock, and they are closely associated with a quasi-monochromatic, finite amplitude Alfvén wave. We suggest that a close relation exists between the nonlinear Alfvén wave and the current tubes as a result of a filamentation instability which is expected to occur at β ≥ 1 and for frequencies comparable to the ion cyclotron frequencies.