Lagrange identification of absolutely unstable regimes in wakes

Abstract

The development of a pulsewise perturbation in a two-dimensional incompressible wake is simulatd numerically using a vortex dynamics method. The main attraction of using vortex methods lies in their Lagrangian nature, which in inviscid flows preserves the identity of rotational fluid elements and thereby allows for the tracking of individual vortex lines or tubes. Because of the non-linearity of this novel approach to identify regions of local absolute and local converctive instability, the analysis is not restricted tio small amplitudes. Moreover the basic state does not have to be locally parallel, and the method is easily applicable to unsteady flows. A comparison of the resulting stability features of the symmetric wake profiles as determined by the numerical simulation with the prediction of the Orr-Sommerfeld analysis confirms the validity of the linear, local stability theory. An extension of the vortex dynamics method to rotational flow fields in which the effects of viscosity become important is enabled by the particle strength exchange scheme.