Gamma ($\gamma$) instability theory, originally proposed in 2003, continues to provide the most promising explanation of salt-fingering engendered thermohaline staircases that are ubiquitously present in both the global ocean and lakes. Our purpose herein is to extend $\gamma$ instability theory to salt-fingering systems in which the vertical gradients of temperature and salinity are not constant. Our goal is to explain why the characteristic “step size” in a salt-fingering staircase is larger in regions characterized by weak gradients. Through application of an appropriately modified linear stability analysis, we first demonstrate that the most quickly growing mode of instability is unaltered by the inhomogeneity of the background stratification in most cases. We then perform numerical simulations based upon the mean field equations to show that staircases tend to form and thereafter merge much more quickly in the low gradient regions than the high gradient regions. After explaining this difference of timescale within the framework of our model, we argue that the differences in background gradients of physical properties may arise naturally in a quasiequilibrium staircase environment. We further invoke observations from the Tyrrhenian Sea to support a quasiequilibrium staircase hypothesis.

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• Convection
• Flow instability
• Oceanography
• Transition to turbulence
• Navier-Stokes equation