We present a relatively simple, deterministic, theoretical model for the sublayer streaks in a turbulent boundary layer based on an analogy with Klebanoff modes. Our approach is to generate the streamwise vortices found in the buffer layer by means of a vorticity source in the form of a fictitious body force. It is found that the strongest streaks correspond to a spanwise wavelength that lies within the range of the experimentally observed values for the statistical mean streak spacing. We also present results showing the effect of streamwise pressure gradient, Reynolds number and wall compliance on the sublayer streaks. The theoretical predictions for the effects of wall compliance on the streak characteristics agree well with experimental data. Our proposed theoretical model for the quasi-periodic bursting cycle is also described, which places the streak modelling in context. The proposed bursting process is as follows: (i) streamwise vortices generate sublayer streaks and other vortical elements generate propagating plane waves, (ii) when the streaks reach a sufficient amplitude, they interact nonlinearly with the plane waves to produce oblique waves that exhibit transient growth, and (iii) the oblique waves interact nonlinearly with the plane wave to generate streamwise vortices; these in turn generate the sublayer streaks and so the cycle is renewed.

A micro-valve pulsed-jet vortex-generator driven by piezoelectric actuation was successfully modelled numerically to determine the feasibility of such a design. This includes: modelling the dynamic motion of a unimorph cantilever and the fluid-structure interaction occurring between the unimorph and the fluid flowing over such a structure; the unsteady developing channel flow that would occur through the outlet orifice was also modelled. The initial design was found to have several fundamental flaws that were shown to be easily remedied. The fluid-structure interaction was found to have a strong effect on the motion of the piezoelectric beam and therefore the performance of the pulsed-jet actuator. The response time of the actuator was found to be governed by the micro-valve opening rather than the time taken to establish the jet. However, the resistance of the pulsed-jet actuator was shown to be governed by the outlet orifice; it was an order of magnitude larger than the resistance of the micro-valve.

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