When warm salty water lies above cold fresh water, vertical fingers of salty or fresh water can develop at the interface with a characteristic width of a few centimeters and height of a few meters. This mixing, which is readily observable in laboratory tank experiments, occurs because of a scale-selective instability related to the different diffusion rates of heat and salt in water (heat diffuses about 100 times faster). The rapid diffusion of heat allows the energy locked up in the unstable temperature gradient to be released on small scales, even though the total density gradient is stable. Since sunlight heats the upper ocean and also causes enhanced salinity through evaporation, it is not suprising that much of the world ocean is fingering favorable. Observational evidence of salt fingers in the ocean is conflicting, but many oceanographers today believe that salt fingering plays a major role in water mass mixing and that hence this centimeter-scale phenomena could significantly influence global ocean circulation.
An idealized analytical model, consisting of a few equations, was proposed several decades ago to approximately explain the dynamic instability that leads to observed salt finger phenomena. The results of the model were shown to compare favorably with observed phenomena in salt finger experiments, and similar studies based on this model have followed since. I considered a mathematical approximation used in previous analyses of the model in which transient effects were neglected (a typical approximation in geophysical fluid dynamics stability analyses). I found that when the approximation was not made (i.e., transient effects were included), the results of the model changed significantly, leading to model predictions that agree less well with observations. This suggests that the classic idealized model may not be accurately capturing the key phenomena responsible for salt fingering.