Initial response of a turbulent channel flow to spanwise oscillation of the walls

Abstract

The transient behaviour of a turbulent channel flow suddenly subjected to spanwise harmonic oscillations of the walls is numerically studied by means of direct numerical simulations of the incompressible Navier-Stokes equations. It is well known that this movement of the walls produces a sustained and significant reduction in turbulent friction; in this paper we focus on the early stages of the motion after the start of the oscillations when the fully developed state has not yet established.

It is found that at the very beginning of the oscillatory motion the streamwise wall shear-stress remains constant for a short time interval, the length of which depends on the parameters defining the oscillation. A spanwise velocity profile starts to develop, almost coincident with the analytical laminar solution for the sudden start-up of harmonic oscillations of the wall.

The spanwise flow fully adapts to the new forcing after about one oscillation period, whilst the longitudinal flow is still evolving towards its long-term drag-reducing condition. The duration of the transient for the longitudinal wall shear-stress is significantly longer, and is found to be independent from the oscillation period, at least for the range of periods considered, but to be notably related to the maximum wall velocity. The implications of this last new finding are noteworthy, since it appears that some of the available experimental data concerning drag reduction measurements over an oscillating wall might be biased by transient effects, especially for the highest values of wall velocity.

Moreover, we observe that the turbulent wall friction and the turbulence statistics change from their initial condition to their long-term behaviour following a non-monotonic path. The paper concludes with two- and three-dimensional flow visualizations of the turbulent flow fields immediately after the start of the oscillations. The use of a moving reference frame, in motion with a speed that is comparable to the convection velocity of the turbulent structures in the near-wall region, allows a clear appreciation of the dynamics of the turbulent flow, thanks to the removal of the purely convective motion. The laminar spanwise flow is removed from the computed turbulent flow fields, in order to clarify the dynamics of the near-wall turbulent structures. The initial interaction of turbulence with the moving wall is then vividly described.

Present address: Department of Mathematics, Imperial College, 180 Queen's Gate, London SW7 2BZ, UK.

Notes

Present address: Department of Mathematics, Imperial College, 180 Queen's Gate, London SW7 2BZ, UK.