Validation of a spatially interconnected model for plane poiseuille flow transition control

A novel linearized model for the transition control problem in plane Poiseuille flow has been proposed recently. The model is based on a finite difference approach in streamwise direction and a spectral approach in wall normal direction. It is thus valid for all spatial frequencies and can be used for the synthesis of controllers for flow control problems, using recently developed ideas for spatially interconnected systems. In this paper the above model is validated in both time and frequency domain. For time domain validation, the transient energy is calculated and compared with previously published results. The frequency domain validation is based on nonlinear simulation: a sinusoidal disturbance is applied at the lower boundary and its effect at different locations of the channel are simulated. From a Fourier analysis of the simulated responses, the spatial and temporal frequency responses are obtained and compared with the linearized model. The results suggest that the model captures the dominant features of the problem and can be used for the design of spatially interconnected controllers.