title: Phase relationship in laminar channel flow controlled by traveling-wave-like blowing or suction.
abstract: The phase relationship between the streamwise and the wall-normal velocity disturbances induced by a traveling-wave-like blowing or suction control [T. Min, J. Fluid Mech. 558, 309 (2006)] in a two-dimensional laminar Poiseuille flow is investigated. The investigation is done by solving the linearized Navier-Stokes equation and by using the identity equation between the skin-friction drag and the Reynolds shear stress [K. Fukagata, Phys. Fluids 14, L73 (2002)]. It has been known that a traveling wave creates a nonquadrature between the velocity disturbances and generates the positive phase shift of the streamwise velocity disturbance in the case of a skin-friction drag reduction. The present analysis further reveals that this nonquadrature consists of an inviscid base phase relationship and a near-wall phase shift induced by the viscosity. The analogy between the present control and Stokes' second problem is discussed. The thickness of the near-wall region in which the viscous phase shift takes place is found to be scaled similarly to the Stokes' second problem.
authors.affiliation: Department of Mechanical Engineering, Keio University, Yokohama 223-8522, Japan.
authors.forename: Hiroya
authors.initials: H
authors.lastname: Mamori
authors.forename: Koji
authors.initials: K
authors.lastname: Fukagata
authors.forename: Jerôme
authors.initials: J
authors.lastname: Hoepffner