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This work describes the measurement through a direct numerical simulation (DNS) of the response of a turbulent flow confined between two planar walls to an impulsive body force. This measurement is performed by considering, for the first time, the dependency of the forcing distance from the wall. A zero-mean white-noise volume forcing is used to probe the turbulent flow, and the response function is obtained by accumulating the space-time correlation between the white forcing and the velocity field.
The interest of this research lies primarily in the context of control theory, where the mean impulse response can have relevant applications in the design of closed-loop control laws which exploit the response function to describe the system dynamics.
The numerical simulations have been performed using a well parallelized DNS solver, whose response measurement procedure has been improved in order to deal with the considerable computational effort. The measurements have been carried out for both a laminar and a turbulent base flow and, for both the cases, the linearity range has been checked at various forcing distances. The impulse response analysis has brought to confirming and extending some important results known in literature. Furthermore the three dimensional visualization of the response has allowed the identification of the topology of the interaction mechanisms between the body forcing and the flow.