A synthetic jet pump and a method of pumping fluid using such a synthetic jet pump are disclosed. The synthetic jet pump includes a plurality of first stacks disposed in a series arrangement relative to each other, and a plurality of first valves. A first stack of the plurality of first stacks includes a plurality of first connector pairs coupled to a first support structure and a plurality of first bimorph pairs. The first connector pairs and the first bimorph pairs are disposed in a parallel arrangement relative to each other respectively. A bimorph of one of the first bimorph pairs is coupled to a corresponding first connector pair. The plurality of first valves is disposed at an upstream end of the plurality of first stacks. A valve of the plurality of first valves is movably coupled to a corresponding connector of the plurality of the first connector pairs.