Diapycnal Mixing in the Ocean: The Osborn–Cox Model

Abstract

The Osborn-Cox model is a simplified tracer variance budget that is a basis for direct estimates of the diapycnal Kv. diffusivity When used to interpret temperature variance dissipation measurements, it indicates Kv to be O(10?5 m2 s?1) in the thermocline?much smaller than the diffusivities found by matching large-scale observations to models or budgets. It is argued that, if the Osborn-Cox model is to describe fluxes in the general circulation, it must describe the variance budget of all fluctuations around the long-term average used to define the general circulation. Within this framework, the simplifications leading to the Osborn-Cox model are re-examined to find if they still hold and which is most likely to cause Kv errors. Factors examined (and the importance found) are approximations in the Fourier and Ficks diffusion laws (unimportant), accumulation and advection of tracer variance (unimportant except in regions of strong upwelling), variance production by lateral fluxes (dominant at higher latitudes), sampling errors in estimating the mean tracer gradient (unimportant), and turbulent fluxes of variance ?u???2?. Variance production by lateral fluxes is most common where stratification is weak and causes the Osborn?Cox model to overestimate Kv. The triple product, or turbulent flux of variance, represents potential exchanges of variance between the small turbulent scales and larger variability scales. It cannot be dismissed by scale analysis, and relying on the analogy or a hypothesis of scale isolation to neglect this effect makes the Osborn-Cox model a theory to be verified rather than a deduction.