Mode water formation via cabbeling at strained thermohaline fronts

A simple analytical model is used to elucidate a potential mechanism for steady state mode water formation at a thermohaline front that involves frontogenesis, submesoscale lateral mixing, and cabbeling. This mechanism is motivated in part by recent observations of an extremely sharp, density-compensated front at the North Wall of the Gulf Stream. Here, the inter-gyre, along-isopycnal salinity/temperature difference is compressed into a span of a few kilometers making the flow susceptible to cabbeling. The sharpness of the front is caused by frontogenetic strain, which is presumably balanced by submesoscale lateral mixing processes. We study this balance with our simple model and derive a scaling for the amount of water mass transformation resulting from the ensuing cabbeling. The transformation scales with the strain rate, equilibrated width of the front, and the square of the isopycnal temperature contrast across the front. At the major ocean fronts where mode waters are found, this isopycnal temperature contrast decreases with increasing density near the isopycnal layers where mode waters reside. This implies that cabbeling should result in a convergent diapycnal mass flux into mode water density classes. The scaling for the transformation suggests that at these fronts the process could induce 0.01-1 m² s^-1 of mode water formation per unit length of front in regions of frontogenetic strain.