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The performance of a two-dimensional micro synthetic jet actuator is evaluated using computational modeling and simulation. A synthetic jet is a zero net mass flux device having a cavity with an oscillating membrane as a sidewall. The motion of the membrane produces a fluctuating jet flow, which transfers linear momentum to the external domain. A Navier-Stokes solver that can run on moving and deforming meshes is used to study the membrane-driven flow in and out of the micro cavity geometry. The primary focus of the present investigation is on the delineation of a feasible design space defined by the geometric and actuation parameters that directly affect its performance. The design variables are selected to be the membrane's oscillation frequency and amplitude, the orifice's width and height, and the cavity's width and height. The results clearly indicate that, for a micro synthetic jet discharging into a quiescent medium, these variables have significant control on the vortex formation, its size, its circulation and its momentum flux. Therefore, the desired actuation can be obtained by manipulating these design variables.