Double-component convection due to different boundary conditions with broken reflection symmetry for a component

TL;DR

This paper investigates double-component convection with broken symmetry in boundary conditions, revealing universal oscillatory behavior, abrupt stability changes, and mechanisms for three-dimensionality, with implications for climate change.

Contribution

It introduces new insights into how broken boundary symmetry affects convection stability, including oscillatory persistence and three-dimensional instability mechanisms.

Findings

Broken symmetry leads to persistent oscillatory convection.

Abrupt stability curve changes occur with zero thresholds in inviscid fluids.

New mechanisms for three-dimensionality and hysteresis are identified.

Abstract

Onset of double-component convection due to different boundary conditions is studied in a diversely oriented infinite slot with broken reflection symmetry between the slot conditions for a component. Among other outcomes, the broken symmetry results in small-amplitude viscous convection remaining of an oscillatory nature for any slot orientation other than a horizontal one. Such a universality also involves various abrupt changes in the marginal-stability curves. In inviscid fluid, such changes emerge with zero instability thresholds. Some of these abrupt changes give rise to new mechanisms for three-dimensionality of the instability. One such a mechanism comes with multiplicity and isolated existence of as well as hysteresis between solutions of the linear stability equations. Both the hysteresis region and the other abrupt 3D changes are described in terms of an analogy between the effect of a ratio of the 2D and 3D wave numbers and that of a 2D ratio between two gravity components. The mechanism of finite-amplitude steady convection in a horizontal slot is also analyzed and its relevance to abrupt climate change is discussed. (This is a substantially shortened Abstract. The full version of Abstract is on the manuscript itself.)