Laboratoire d'Hydrodynamique, CNRS-UMR 7646, École Polytechnique,
F-91128 Palaiseau Cedex, France
Nonlinear convective/absolute instabilities in parallel two-dimensional
wakes
Phys. Fluids10(11: Nov. 1998), 2724-2736.
Abstract:
The linear versus nonlinear convective/absolute instability of a family
of plane wake profiles at low Reynolds number is investigated by numerically
comparing the linearized and the fully nonlinear impulse responses. Through
an analysis of the linear flow response obtained by DNS, the linear temporal
and spatio-temporal instability properties are retrieved, in excellent
agreement with the properties obtained by Monkewitz from the study of the
associated viscous dispersion relation. Nonlinear terms are then shown
to limit the amplitude to a saturation level within the response wavepacket,
while leaving the trailing and leading edges unaffected. For this family
of open shear flows, the velocities of the fronts, formed between the trailing
or leading edge and the central saturated region, are thus selected according
to the linear Dee & Langer criterion, whereas the front solutions are
fully nonlinear. This property may be of importance in justifying the use
of linear instability properties to predict the onset and the frequency
of the von Kármán vortex street.