Nonlinear dynamics and hydrodynamic feedback in two-dimensional double cavity flow

Abstract

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.