What determines the thickness of layers in a thermohaline staircase?

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 (Ho). 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 Ho. 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.