Bistability of buoyancy-driven exchange flows in vertical tubes

TL;DR

This study demonstrates that buoyancy-driven exchange flows in vertical tubes are inherently bistable, with two possible flow states, challenging previous models that assumed a unique solution and impacting interpretations of natural and engineering systems.

Contribution

The paper introduces a bistability model for buoyancy-driven exchange flows and validates it through numerical simulations that align with experimental data, revealing two stable flow configurations.

Findings

Buoyancy-driven exchange flows are inherently bistable.

Numerical simulations match experimental data without fitting parameters.

Flow switching between two states is possible in such systems.

Abstract

Buoyancy-driven exchange flows are common to a variety of natural and engineering systems ranging from persistently active volcanoes to counterflows in oceanic straits. Experiments of exchange flows in closed vertical tubes have been used as surrogates to elucidate the basic features of such flows. The resulting data have historically been analyzed and interpreted through core-annular flow solutions, the most common flow configuration at finite viscosity contrasts. These models have been successful in fitting experimental data, but less effective at explaining the variability observed in natural systems. In this paper, we formulate a core-annular solution to the classical problem of buoyancy-driven exchange flows in vertical tubes. The model posits the existence of two mathematically valid solutions, i.e. thin- and thick-core solutions. The theoretical existence of two solutions, however, does not necessarily imply that the system is bistable in the sense that flow switching may occur. Using direct numerical simulations, we test the hypothesis that core-annular flow in vertical tubes is bistable, which implies that the realized flow field is not uniquely defined by the material parameters of the flow. Our numerical experiments, which fully predict experimental data without fitting parameters, demonstrate that buoyancy-driven exchange flows are indeed inherently bistable systems. This finding is consistent with previous experimental data, but in contrast to the underlying hypothesis of previous analytical models that the solution is unique and can be identified by maximizing the flux or extremizing the dissipation in the system. These results have important implications for data interpretation by analytical models, and may also have relevant ramifications for understanding volcanic degassing.