Some oceanographic mixing parameterizations assume that transports depend nonlinearly on the buoyancy gradient; e.g., diffusivities are proportional to some power of the buoyancy gradient. In this paper we examine the consequences of these nonlinear-diffusion parameterizations by solving an initial value problem in which the t = 0 thermohaline fields are prepared as random and uncorrelated distributions of temperature and salinity. Solutions of the nonlinear diffusion equation as a ‘rundown’ problem show that correlations develop between the temperature and salinity. These correlations are such that the evolving thermohaline gradients tend to be strongly compensating in their joint effect on buoyancy.
Ferrari, Raffaele, and W. R. Young. 1997. "On the development of thermohaline correlations as a result of nonlinear diffusive parameterizations." Journal of Marine Research 55, (6). https://elischolar.library.yale.edu/journal_of_marine_research/2255