The auroral ionospheric E-region supports at least two types of plasma irregularities: the gradient drift instability and the Farley-Buneman instability. These are driven by the electron density gradient and the electric field, respectively. In this paper we study the effect of the three-dimensional auroral geometry on the saturation of the instabilities. For that purpose, an exact stationary solution to the two-fluid plasma model equations is derived. The stationary state thus obtained is used as an initial condition of a three-dimensional nonlinear fluid simulation. The algorithm is also described. In the auroral zone, the collision frequencies have gradients along the magnetic field. This implies that the phase velocity of the plasmons depends on the altitude, which in turns causes wave propagation at a nonzero aspect angle. These waves are more damped than exactly perpendicular ones. From this it is no surprise that our three-dimensional code can be used even when the electric field is near the Farley-Buneman threshold value. On the contrary, two-dimensional fluid algorithms blow up when the electric field is that large. We also conclude that the height profiles of the electric field, the electron density and the collision frequencies all affect coherent radar spectra, alongside with the local value of the electric field.