The nonlinear dynamics following saturation of the parametric instabilities of a monochromatic field-aligned large-amplitude circularly polarized Alfv¿n wave is investigated via direct numerical simulation in the case of high plasma &bgr; and no wave dispersion. The magnetohydrodynamic (MHD) code permits nonlinear couplings in the parallel direction to the ambient magnetic field and one perpendicular direction. Compressibility is included in the form of a polytropic equation of state. Turbulent cascades develop after saturation of two coupled oblique three-wave parametric instabilities; one of which is an oblique filamentationlike instability reported earlier. Remnants of the parametric processes, as well as of the original Alfv¿n pump wave, persist during late nonlinear times. Nearly incompressible MHD features such as spectral anisotropies appear as well.