The problem of coherent perturbations in a turbulent mixing layer is revisited. The governing equations for perturbations are derived from the RANS equations with a Boussinesq-type closure model. The proposed theoretical model utilizes the idea of separating the "fast" and the "slow" scales in a manner similar to the PSE concept. However, the equations for the amplitude functions are not simplified (not parabolized). Emulation of an actuator (oscillating flap) is introduced into the computational analysis via inhomogeneous boundary conditions. The actuator size and amplitude, the effect of coherent perturbation on the base flow, and the non-linear effects in the development of the coherent signal are investigated.