An experimental study of ion acoustic plasma turbulence in a collision-dominated positive column is presented. Linear theory predictions, which include ion Landau damping and the effects of a dc electric field, are shown to agree with measured values of convective growth rates. At high levels of turbulence, interferometric methods are not useful for studying the wave phase characteristics. Instead, the detailed spectral density for two-dimensional wave propagation, S (k,ω), is obtained by performing a two-dimensional spatial Fourier transform on sampled values of the frequency sweeps of the complex cross-power spectral density. The instability is found to be essentially one-dimensional, with the waves propagating along the direction of the electron drift velocity. The spectra are integrated numerically, and the energy density obtained is discussed in terms of two nonlinear models of saturated state of the instability. Time- and frequency-resolved power spectra are measured by sampling techniques, and compared to the predictions of linear theory. Temporal evolution of the phase characteristics is measured by a novel diagnostic technique.