Diapycnal Mixing in the Ocean: Equations for Large-Scale Budgets

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Abstract
The Osborn–Cox model is the basis for the most direct estimates of the diapycnal diffusivity Kv for tracers. When used to interpret temperature variance dissipation measurements, it leads to Kv of O (10−5 m2 s−1) or less in the main thermocline. Large-scale diagnostic models typically match observations best using Kv of O (10−4 m2 s−1). The framework for describing diapycnal fluxes of tracers like temperature or density from large-scale property distributions is reexamined in an attempt to discover possible causes for this disagreement. Starting from basic thermodynamics principles, suitable tracer conservation equations are developed and the simplifications leading to conventional mean-field and variance balances are examined. It is argued that separation of mean and eddy fields is best based on long but finite time averages rather than the usual space-scale separation. Because this separation leads to a more vigorous eddy field than the usual procedure it is necessary to reexamine all conventional simplifications. The usual approximate descriptions of molecular transport are found adequate. Direct effects of molecular fluxes are important only in the density equation where they lead to a density source that cannot be expressed as a flux divergence. Observed large-scale time changes of temperature and salinity are so large that inferring diapycnal diffusivities of O (10−5 m2 s−1) is difficult even from multilayer averages. On horizontal scales of hundreds of kilometers, lateral eddy fluxes of heat and salt are so large that it is nearly impossible to accurately determine a Kv of O (10−5 m2 s−1) from local potential temperature or salt budgets. The density source is comparable to the divergence of turbulent density fluxes and confuses inference of Kv from potential density budgets. This source also causes the velocity field to be slightly divergent, confusing inference of vertical velocity from observations of horizontal flow.

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