ngineering applications of unsteady boundary layers are numerous and of great importance in hydro and aero dynamics. Relatively little research however is focussed on understanding the flow structure if the perturbations in the flow are caused by the motion of flexible boundaries rather than by time dependent variations in the flow itself. A model is therefore developed to examine the hydrodynamic characteristics of external laminar flow over an arbitrarily shaped body, a portion of which is subjected to harmonic motion. A vorticity-stream function formulation of the Navier-Stokes equations is used. A boundary fitted coordinate system is adopted to allow accurate modeling in the presence of the time dependent motion of the body surface. The flow equations are solved using a Thompson Tri Diagonal Finite Difference Algorithm. Inviscid-viscous interaction theory is used to split the model domain and save computational time. The model is tested by comparison to selected numerical, experimental or analytical results for flow over a cavity, boundary layer flow along a flat plate and time dependent flow in a channel with wavy walls. The model is then applied to predict the flow over a flat plate and circular cylinder with a section forced in simple harmonic motion. The nonlinear response of the flow is investigated for various Reynolds numbers, Re, Strouhal number, St, (ratio of the flow advective time scale to the plate or cylinder oscillation period), vibration amplitude ration,
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