Surface dielectric barrier discharges (sDBD) are efficient and scalable plasma sources for plasma-based gas conversion. One prominent feature of an sDBD is the generation of an ion wind, which exerts a force on the neutrals, thus leading to an efficient mixing of plasma and a passing gas stream. This becomes apparent by the creation of upstream and downstream vortices in the vicinity of the plasma. In this study, these vortices are generated by high voltage burst pulses consisting of two half cycles of an almost sinusoidal voltage shape. The vortices are monitored by Schlieren imaging diagnostic to benchmark and connect two simulations of the sDBD: a plasma model simulating a streamer for 25 ns starting from the electrode and propagating along a dielectric surface followed by a decay. The streamer is the source of electrical charges accelerated as ion wind by the applied electric field from the sDBD power supply. A second flow simulation models this ion wind as a time-averaged thrust acting on the passing gas stream. The conversion of the time-resolved forces from the nanosecond plasma simulation into the steady state thrust in the flow simulation indicates that the force from the plasma lasts much longer than the actual streamer propagation phase. This is explained by the fact that the charges in the streamer channel remain present for almost 100 ns, and the voltage from the power supply lasts for a few microseconds being applied to the electrode so that ions in the streamer channel are still accelerated even after a streamer stops to propagate after a few ns. The thrust generated during the streamer phase, including the relaxation phase, agrees well with predictions from flow simulation. Additionally, properly converting the time-resolved forces from the plasma simulation into a time-averaged thrust for the flow simulation yields exactly the synthetic Schlieren images as measured in the experiments.