Control of Structures and Time-Averaged Flow Properties of a Plane Wake by Subharmonic Instability Modes.

Abstract

In the present work, structures and time-averaged flow properties in the transition region of a plane wake perturbed by the unstable subharmonic modes were studied by means of direct numerical simulations. The incompressible time-dependent 2-D Navier-Stokes equations were solved using Pade finite difference approximations in the streamwise direction, a mapped pseudospectral Fourier method in the cross-stream direction, and a third-order compact Runge-Kutta scheme for time advancement. The unstable modes (fundamental mode and its subharmonics) of the Orr-Sommerfeld equations were used to perturb a Gaussian wake of the inlet plane. The statistics of the wake forced by the unstable modes and the corresponding numerical structures of the vortices are presented. When the wake is forced by the fundamental mode and its two subharmonics with large amplitudes, the dominant evolution of the fundamental mode is responsible for the clear alternating sign vortices and the downstream statistics. After the fundamental mode saturates, the subharmonic components grow downstream. Further downstream, the influence of the first subharmonics on the vortex street and the turbulent statistics are observed. The downstream evolutions of Reynolds stresses are governed by the growth of the subharmonics. The cross-stream profiles of the Reynolds stresses are asymmetric because of the spatial evolution of the first subharmonics.