Hamid Ait Abderrahmane

Applying nonlinear dynamic theory to one-dimensional pulsating detonations

The dynamical behaviour of one-dimensional pulsating detonations was investigated in detail, with the aid of nonlinear theory tools such as phase plots and correlation dimension. The period-doubling cascade, as routes to deterministic chaos, is depicted through the transformations of the shapes of the attractors. Using a correlation dimension method, the dimension of the attractors is determined and we show that the chaos within a one-dimensional pulsating detonation is deterministic.

FRACTAL GEOMETRY OF THE WAKE SHED BY A FLAPPING FILAMENT IN FLOWING SOAP-FILM

In this study, we illustrate the fractal nature of the wake shed by a periodically flapping filament. Such wake structure is a combination of primary vortex shedding resulting in the von Karman vortex street, a series of concentrated vortex dipoles formed when the trailing edges of filaments reach their maximum amplitudes and small eddies form along the shear layer connected with the concentrated vortices due to the shear layer instability. The vortex dynamics of the flapping filament are visualized and imaged experimentally using a soap-film flow tunnel with a high-speed camera and a low pressure sodium lamp as a light source. The wake fractal geometry is measured using the standard box-counting method and it is shown that the fractal dimension of the soap pattern boundaries in the wake is D = 1.38 ± 0.05, which agrees well with those measured for fully developed turbulences and other shear flow phenomena. The invariant of the fractality in the wake induced by the flapping filament thus provides another illustration of the geometrical self-similarity and nonlinear dynamics of chaotic fluid flows.