Numerical simulations of the generalized Rayleigh-Taylor instability are presented. The model and simulations are applicable to bottomside and topside spread F, unstable barium cloud dynamics, and collisional interchange instability in general. The principal result is that the evolution of the instability tends to an anisotropic state consisting of nearly sinusoidal (quasi-periodic) variation along the effective electric field, and shocklike structures propagating perpendicular to Eeff along the extrema of the quasiperiodic structures. The spectral properties of the nonlinear state are analyzed using one-dimensional power spectra calculated along spatial trajectories for selected angles to Eeff . In this way a direct comparison to in situ probe data can be made. The inherent anisotropy of the nonlinear state is reflected in major qualitative differences between the spectra taken parallel to and perpendicular to Eeff . The fundamental finding of the present work is that anisotropy in interchange dynamics is much greater than had been previously reported. This strong anisotropy can explain much of the spectral and spatial structural characteristics of both bottomside and topside spread F. In a companion paper a comparison of the simulation results to various in situ data sets is given.