Flow field topology of buoyancy induced mixing

Abstract

We consider the global topology of a flow field produced by buoyancy in stretching and folding a material interface inside a cavity through numerical experiments. The buoyancy induced flow field for the parametric region of interest stretches and folds the interface into whorl structures followed by transient oscillations and stable stratification. Final mixing after stratification occurs by mass diffusion. From the solution of the flow field, its global topology is examined by finding its critical points and corresponding integral manifolds. Two types of critical points occur, elliptic and hyperbolic. We show that during stretching and folding of the interface a series of bifurcations occur which involve homoclinic and heteroclinic orbits connecting the hyperbolic critical points. These orbits are structurally unstable and form resonance or stochastic regions. Due to oscillatory nature of the flow, local mixing occurs through a series of explosive and catastrophic bifurcations. The explosive bifurcations yield chaotic orbits whereas annihilation of the seperatrixes occur during the catastrophic bifurcations. Superposition of forward and backward mapping of the interface structure corresponding to the stochastic region shows that the flow produces horseshoe maps. This indicates that local mixing is produced by a chaotic transient. However, microgravity conditions indicate that there exists a single elliptic point in the flow field, and mixing occurs diffusively without stretching the interface.