What determines the thickness of layers in a thermohaline staircase?

Abstract

A simple theory is developed for the equilibrium height of steps in a thermohaline staircase. The model is based on a linear stability analysis for a series of salt-finger interfaces, which reveals a tendency for the staircase to evolve in time until the characteristic thickness of layers reaches a critical value ($H_0$). Relatively thin layers successively merge as a result of the parametric variation of the heat/salt flux ratio ($\gamma$), but these mergers cease when the thickness of layers exceeds $H_0$. The equilibration of thick steps in our model is caused by the slight inhomogeneity of the convecting layers which has a stabilizing effect on the staircase. The instability theory is successfully tested against fully nonlinear numerical simulations and is qualitatively consistent with oceanic observations.