TY - JOUR

T1 - Phase relationship in laminar channel flow controlled by traveling-wave-like blowing or suction

AU - Mamori, Hiroya

AU - Fukagata, Koji

AU - Hoepffner, Jerôme

PY - 2010/4/9

Y1 - 2010/4/9

N2 - The phase relationship between the streamwise and the wall-normal velocity disturbances induced by a traveling-wave-like blowing or suction control 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. 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.

AB - The phase relationship between the streamwise and the wall-normal velocity disturbances induced by a traveling-wave-like blowing or suction control 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. 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.

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U2 - 10.1103/PhysRevE.81.046304

DO - 10.1103/PhysRevE.81.046304

M3 - Article

AN - SCOPUS:77950960441

VL - 81

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 4

M1 - 046304

ER -