## What determines the thickness of layers in a thermohaline staircase?(English)Zbl 1065.76087

Summary: 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, 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.

### MSC:

 7.6e+18 Interfacial stability and instability in hydrodynamic stability

### Keywords:

linear stability analysis; salt-finger interfaces
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