Drag reduction in incompressible channel flow using electromagnetic forcing

Abstract

This work focuses on feedback control of incompressible transitional Newtonian channel flow described by two-dimensional Navier-Stokes equations. The control system uses measurements of shear stresses on the lower channel wall and the control actuation is assumed to be in the form of electromagnetic Lorentz forces applied to the flow near the bottom wall. Galerkin's method is initially used to derive a finite-dimensional approximation of the flow field which is subsequently used for the synthesis of an output feedback controller that enforces stability in the closed-loop system. The controller is applied to a simulated transitional channel flow and is shown to significantly reduce the drag on the lower channel wall.