Salt fingering staircases and the three-component Phillips effect

TL;DR

This paper extends the Phillips effect theory to a three-component salt fingering system, developing a nonlinear model that predicts the formation, evolution, and merging of salt fingering staircases using a regularized approach.

Contribution

It introduces the first nonlinear, regularized model for salt fingering staircases based on the generalized Phillips effect in a three-component system.

Findings

Model predicts the onset of layering within specific parameter ranges.

Layered structures form from initial linear instability and merge over time.

Mergers enhance buoyancy gradients and fluxes across interfaces.

Abstract

Understanding the dynamics of staircases in salt fingering convection presents a long-standing theoretical challenge to fluid dynamicists. Although there has been significant progress, particularly through numerical simulations, there are a number of conflicting theoretical explanations as to the driving mechanism underlying staircase formation. The Phillips effect proposes that layering in stirred stratified flow is due to an antidiffusive process, and it has been suggested that this mechanism may also be responsible for salt fingering staircases. However, the details of this process, as well as mathematical models to predict the evolution and merger dynamics of staircases, have yet to be developed. We generalise the theory of the Phillips effect to a three-component system (e.g. temperature, salinity, energy) and demonstrate the first regularised nonlinear model of layering based on mixing-length parameterisations. The model predicts both the inception of layering and its long-term evolution through mergers , whilst generalising, and remaining consistent with, previous results for double-diffusive layering based on flux ratios. Our model of salt fingering is formulated using spatial averaging processes and closed by a mixing length parameterised in terms of the kinetic energy and the salt and temperature gradients. The model predicts a layering instability 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 merge through a process of stronger interfaces growing at the expense of weaker interfaces. Mergers increase the buoyancy gradient across interfaces, and increase the buoyancy flux through the staircase.