Can vertical mixing arrest ocean frontogenesis?

Abstract

Frontogenesis is the process by which ocean fronts--regions of strong horizontal density gradients in the upper ocean--strengthen. It is a highly non-linear phenomenon arising from many competing effects, such as background strain, instabilities, and surface forcing. Vertical mixing plays a complicated role in governing both frontogenesis and the long-term dynamics of ocean fronts. For weak fronts, it has been shown to drive shear dispersion which further weakens the front over long timescales. However, vertical mixing also mixes the vertically-sheared thermal wind velocity, driving the front out of balance and causing a secondary circulation to develop that may strengthen the front. Here, it is shown that vertical mixing can directly act to oppose the frontogenetic secondary circulation, provided the frontal width is larger than a critical value. A non-linear iteration method is described for finding balanced states in which vertical mixing arrests frontogenesis and the parameter dependence of this regime is discussed. Further, existing asymptotic solutions for the buoyancy and velocity fields are extended and found to closely match these balanced states, even outside their region of formal validity.