Linear-regime Ar+ bombardment of Si produces symmetrical ripple structures at ion incidence angles above 45° measured off-normal (Madi 2009 J. Phys.: Condens. Matter 21). In the nonlinear regime, new behaviors emerge. In this paper, we present experimental results of ion bombardment that continues into the nonlinear regime until pattern saturation at multiple ion incidence angles, showing the evolution of their grazing incidence small-angle x-ray scattering (GISAXS) spectra as well as atomic force microscopy topographs of the final, saturated structures. Asymmetric structures emerge parallel to the direction of the projected ion beam on the sample surface, constituting a height asymmetry not found in the linear regime. We then present simulations of surface height evolution under ion bombardment using a nonlinear partial differential equation developed by Pearson and Bradley (2015 J. Phys.: Condens. Matter 27 015010). We present simulated GISAXS spectra from these simulations, as well as simulated scattering from a sawtooth structure using the FitGISAXS software package (Babonneau 2010 J. Appl. Crystallogr. 43 929-36), and compare the simulated spectra to those observed experimentally. We find that these simulations reproduce many features of the sawtooth structures, as well as the nearly-flat final GISAXS spectra observed experimentally perpendicular to the sawtooth structures. However, the model fails to reproduce the final GISAXS spectra observed parallel to the sawtooth structures.