周期運動の安定化による低レイノルズ数平面クエット乱流の抵抗低減(乱流(4),一般講演)

概要

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Unstable gentle periodic motion has recently been found in plane Couette flow (J. Fluid Mech. 449, 291 (2001)]. Since this periodic motion exhibits smaller skin friction drag than turbulent flow, it could be useful as a target state for reduction of skin friction drag of turbulence. In this study, the gentle periodic solution is recomputed by using the Newton-GMRES method to be used for drag reduction in turbulent plane Couette flow at the Reynolds number Re=400. In finite-difference-based direct numerical simulations, possibility of stabilization of the periodic motion is examined by imposing external body force, κ_c(u_p-u) per unit mass (κ_c, u_p, and u being the gain constant, the velocity field of the periodic motion and the velocity of a flow state to be controlled, respectively), localized in the near-wall region. The minimal height of the region for stabilization is evaluated at several values of the gain constant for distinct dimensions of a computational periodic domain. It is found that the minimal height for stabilization is invariant for the streamwise and spanwise dimensions of the domain; (2L_x, L_z), (4L_x, L_z), (2L_x, 2L_z) (L_x and L_z being the streamwise and spanwise period of the periodic motion, respectively), implying that the drag reduction could be accomplished in a large domain by localized forcing.
2010-09-09