We report on highly time- and space-resolved measurements of the evolution of electron plasma waves driven by stimulated Raman scattering of a picosecond, single laser speckle propagating through a preformed underdense plasma. Two-dimensional Thomson scatter spectra indicate that the dominant waves have significant transverse components. These results are supported by particle-in-cell simulations which pinpoint the dominant role of the wave front bowing and of secondary nonlinear electrostatic instabilities in the evolution of the plasma waves.