Numerical simulation of the absolutely and convectively unstable wake

Abstract

The development of the wake behind a flat plate at a supercritical Reynolds number (Re= 200, based on the plate thickness and free-stream velocity) is simulated numerically by solving the two-dimensional unsteady Navier-Stokes equations with a finite-difference Galerkin method. The intermediate quasi-steady state of the wake development is investigated with an Orr-Sommerfeld analysis for complex frequencies and wavenumbers. Based on this linear, local stability analysis it can be shown that the quasi-steady state can be divided into regions of local absolute and local convective instability. One goal of this work is to determine the validity of the linear, local stability theory by comparing the predictions of the Orr-Sommerfeld analysis to the results of a numerical wake simulation. Based on this comparison, for the investigated flow field, the frequency selection mechanisms recently proposed by several authors are discussed. Base bleed is applied in the numerical simulation of the wake as a control parameter, following the well-known experimental result that sufficient base bleed reduces the strength of the vortex street (see e.g. Wood 1964). It can be shown that from a critical base-bleed ratio, disturbances grow no longer in time but only in space, indicating a change of the global stability characteristics. In addition the linear, local stability analysis is used to investigate to what extent this global transition can be described.