We present a numerical survey of the nonlinear flavor development of dense neutrino gases. This study is based on the stationary, two-dimensional ($x$ and $z$), two-beam, monochromatic neutrino line model with a periodic boundary condition along the $x$ direction. Similar to a previous work, we find that small-scale flavor structures can develop in a neutrino gas even if the physical conditions are nearly homogeneous along the $x$ axis initially. The power diffusion from the large-scale to small-scale structures increases with the neutrino density and helps to establish a semi-exponential dependence of the magnitudes of the Fourier moments on the corresponding wave numbers. The overall flavor conversion probabilities in the neutrino gases with small initial sinusoidal perturbations reach certain equilibrium values at large distances which are mainly determined by the neutrino-antineutrino asymmetry. Similar phenomena also exist in a neutrino gas with a localized initial perturbation, albeit only inside an expanding flavor conversion region. Our work suggests that a statistical treatment may be possible for the collective flavor oscillations of a dense neutrino gas in a multi-dimensional environment.
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