Abstract

The phenomenon of staircase formation in double-diffusive convection has attracted much interest, with several theories proposed for the mechanism leading to layering. By drawing parallels between the popular γ-instability theory, and the Phillips effect (which leads to layering in stirred stratified fluids), we propose a framework that encapsulates both double-diffusive and stirred layer formation. With a three-component system for temperature, salinity and kinetic energy, a regularised linear stability is predicted, with a well-defined preferred wavenumber.We present a system of one-dimensional equations derived from a horizontal averaging process, for which the stability analysis predicted layering for a bounded range of parameter values in the salt-fingering regime. Nonlinear solutions show that an initially unstable linear buoyancy gradient develops into layers, which proceed to merge through a process of stronger interfaces growing at the expense of weaker ones. Our results indicate that these mergers are responsible for the characteristic increase of buoyancy flux through thermohaline staircases.