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

Hiroya Mamori, Koji Fukagata, and Jerôme Hoepffner
Phys. Rev. E 81, 046304 – Published 9 April 2010

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 et al., 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 et al., 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.

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  • Received 4 August 2009

DOI:https://doi.org/10.1103/PhysRevE.81.046304

©2010 American Physical Society

Authors & Affiliations

Hiroya Mamori1, Koji Fukagata1, and Jerôme Hoepffner2

  • 1Department of Mechanical Engineering, Keio University, Yokohama 223-8522, Japan
  • 2Institut D’Alembert, UPMC, 75252 Paris Cedex 05, France

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Issue

Vol. 81, Iss. 4 — April 2010

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