This paper models the breakup of a circular jet, which is subjected to both pure and composite disturbances using an interface tracking method. The tracking method referred to as the Level-Set Method (LSM), numerically simulates disturbance growth under the same conditions as those in experiments previously published on jet breakup using a piezoelectric actuator. Results from the modeling are compared with the experimental results. Experimentally, the jet is modulated through the axial vibration of an orifice plate. In the model, the axial disturbance is an artificially applied velocity fluctuation at the inlet. Both modeling results and experimental observations of the breakup due to a pure disturbance clearly show formation of large satellites between main droplets at lower frequencies inside the regular breakup regime. Previous experiments showed that practical devices always show generation of interfering disturbances along with the fundamental disturbance, which can have different impacts on the jet breakup. Experimental results are compared with simulation examples studying breakup due to a composite disturbance. Comparison shows that the model clearly accommodates a composite disturbance and it accurately predicts results similar to those seen in experiments. Previous experimental investigations also proposed a composite disturbance as the solution to merge satellites or decrease their size. Although it is practically not possible to measure the actual amplitude magnitude in experiments, the model demonstrates key features and qualitatively shows how the breakup is affected by adding a high frequency mode.