Nonlinear dynamics and hydrodynamic feedback in two dimensional double cavity flow
Résumé
This paper reports results obtained with two-dimensional numerical simulations of
viscous incompressible flow in a symmetric channel with a sudden expansion and
contraction, creating two facing cavities; a so-called double cavity. Based on time
series recorded at discrete probe points inside the double cavity, different flow regimes
are identified when the Reynolds number and the intercavity distance are varied. The
transition from steady to chaotic flow behaviour can in general be summarized as
follows: steady (fixed) point, period-1 limit cycle, intermediate regime (including
quasi-periodicity) and torus breakdown leading to toroidal chaos. The analysis of
the intracavity vorticity reveals a carousel pattern, creating a feedback mechanism,
that influences the shear-layer oscillations and makes it possible to identify in which
regime the flow resides. A relation was found between the ratio of the shear-layer
frequency peaks and the number of small intracavity structures observed in the flow
field of a given regime. The properties of each regime are determined by the interplay
of three characteristic time scales: the turnover time of the large intracavity vortex,
the lifetime of the small intracavity vortex structures and the period of the dominant
shear-layer oscillations.