Plasma turbulence has been shown to play a critical role in many astrophysical and space environments. In the solar corona and solar wind, this turbulence involves the nonlinear interaction of kinetic Alfv en waves. In the Earth's magnetosphere, the turbulence is dominated by inertial Alfv en wave collisions. Observations of these wave-wave interactions in space and in laboratory plasma environments have shown that, in addition to the nonlinear cascade of energy to small scales, the interaction also produces nonlinear beat waves that have a frequency defined by f 6 3 ¼ jf 1 6f 2 j. Although the temporal behavior of the beat wave has been well documented, this paper presents the first detailed analysis of the spatial structure of the nonlinearly generated beat wave. V C 2016 AIP Publishing LLC. [http://dx.