Abstract
In this paper, the effect of a special active control on the Blasius boundary layer is investigated with the Orr-Sommerfeld and the Reynolds-Orr energy equations. The control moves the wall in the streamwise direction proportional to the fluctuating wall shear stress which was proposed by Józsa et al. [“Active and passive in-plane wall fluctuations in turbulent channel flows,” J. Fluid Mech. 866, 689–720 (2019)]. Our results showed that the negative proportional parameters destabilize the flow, while the positive values lead to a contradictory outcome. According to the Orr-Sommerfeld equation, with the right choice of the parameter, the critical Reynolds number can be significantly increased. At the same time, the Reynolds-Orr equation predicts that any streamwise movement of the wall proportional to the wall shear stress slightly destabilizes the flow.
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