The unsteady structure of a supersonic jet is highly three dimensional, though the mean flow is axisymmetric. In simulating a circular jet, the centerline represents a computational boundary. As such, spurious modes can be generated near centerline, unless special attention is given to the behavior of the 3D structure near the centerline. Improper treatment of the dependent variables near the centerline results in the solution diverging or being suitable only for small amplitude excitation. With a careful treatment of the centerline formulation, no spurious mode is generated. The results show that a near linear disturbance growth is obtained, as the linear stability theory indicates. At high levels of excitation, nonlinear development of disturbances is evident and saturation is reached downstream.