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.
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|Publication status||Published - 2010 Apr 9|
ASJC Scopus subject areas
- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Statistics and Probability