The stability of the boundary layer is a fairly addressed problem. We were, however, interested in the influence of plate movement relative to fluid flow. We hypothesized that this could trigger premature vortex formation and faster spread. We addressed the problem with the Orr-Sommerfeld equation of stability and discretization in the $ x $-direction. By searching for the eigenvalues of the system, we searched for the moment of transition to an unstable state. With temporal and spatial analysis, we were also able to observe the rate of spread of instability throughout space. Intermediate results showed that the oscillations have no effect (that the stability depends only on $ Re_\delta $), but later, from further numerical simulations, we concluded that the oscillations have an effect on the propagation of perturbations throughout space. The influence on the moment of transition to instability was observed through the shape of the stability contours.
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