Density-compensated temperature and salinity gradients are often observed in mixed layer fronts. A possible explanation Of this Observation is that there is a systematic relation between the “strength” of a front, defined as the buoyancy jump across the front, and the thickness of a front. If stronger fronts tend to be thicker, then in an ensemble of random fronts, in which the temperature and salinity jumps am independent random variables, the temperature and salinity gradients will he correlated. This correlation between the thermohaline gradients is such that heat and salt make antagonistic contributions to the buoyancy gradient–-that is, them is buoyancy compensation. The statistics of heat and salt fluxes across nearly compensated fronts are counterintuitive: strong heat fluxes can occur across a front with weak thermal gradients and strong salinity gradients, and vice versa.
As a specific model that relates the width of a front to the strength of a front, a pair of coupled nonlinear diffusion equations for heat and salt are used. The nonlinear diffusion coefficient, proportional to the square of the buoyancy gradient, arises from quasi-steady shear dispersion driven by thermohaline gradients. This nonlinear mixing prevents stirring by mesoscale advection from indefinitely filamenting mixed layer tracer distributions. The model predicts that the thickness of a front varies as the square root of the strength and inversely as the one-quarter power of the mesoscale strain.