Author(s)

T. Atobe

Abstract

Influence of wall oscillation on laminar-turbulent transition of the plane Poiseuille flow is investigated analytically and numerically. For the analytical approach, the Floquet theory using a time-dependent Orr-Sommerfeld equation is employed to estimate the fundamental aspect of this flow. The velocity profiles for the analysis are assumed as the superposition of the plane Poiseuille flow and the Stokes layer. Also the collocation method is used in the wallnormal direction for making the monodromy matrix. Depending on the parameters, namely frequencyΩand amplitude Uw of the wall-oscillation, there is the stable region inΩ-Uw plane even though the Reynolds number is of supercritical. Direct numerical simulation (DNS) based on the Fourier spectral method is also employed to confirm the analytical results and to clear the flow structures. The results by DNS show good agreement with the Floquet analysis and also reveal that the vortex structures in the vicinity of the walls are strongly affected by the wall oscillation. Keywords: plane Poiseuille flow, wall oscillation, Floquet analysis, DNS.

Keywords

plane Poiseuille flow, wall oscillation, Floquet analysis, DNS.