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On Geometrical Aspects of Interior Ocean Mixing

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  • 1 School of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales, Australia
  • | 2 Institute for Marine and Atmospheric Studies, University of Tasmania, and CSIRO Marine and Atmospheric Research, Castray Esplanade, Hobart, Tasmania, Australia
  • | 3 NOAA/Geophysical Fluid Dynamics Laboratory, Princeton, New Jersey
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Abstract

The small-slope approximation to the full three-dimensional diffusion tensor of epineutral diffusion gives exactly the same tracer flux as the commonly used projected nonorthogonal diffusive flux of layered ocean models and of theoretical studies. The epineutral diffusion achieved by this small-slope approximation is not exactly in the direction of the correct epineutral tracer gradient. That is, the use of the small-slope approximation leads to a very small flux of tracer in a direction in which there is no epineutral gradient of tracer. For (the tracer) temperature or salinity, the difference between the correct epineutral gradient and the small-slope approximation to it is proportional to neutral helicity. The authors also make the point that small-scale turbulent mixing processes act to diffuse tracers isotropically (i.e., the same in each spatial direction) and hence it is strictly a misnomer to call this process “dianeutral diffusion” or “vertical diffusion.” This realization also has implications for the diffusion tensor.

Corresponding author address: Trevor J. McDougall, School of Mathematics and Statistics, University of New South Wales, NSW 2052, Australia. E-mail: trevor.mcdougall@unsw.edu.au

Abstract

The small-slope approximation to the full three-dimensional diffusion tensor of epineutral diffusion gives exactly the same tracer flux as the commonly used projected nonorthogonal diffusive flux of layered ocean models and of theoretical studies. The epineutral diffusion achieved by this small-slope approximation is not exactly in the direction of the correct epineutral tracer gradient. That is, the use of the small-slope approximation leads to a very small flux of tracer in a direction in which there is no epineutral gradient of tracer. For (the tracer) temperature or salinity, the difference between the correct epineutral gradient and the small-slope approximation to it is proportional to neutral helicity. The authors also make the point that small-scale turbulent mixing processes act to diffuse tracers isotropically (i.e., the same in each spatial direction) and hence it is strictly a misnomer to call this process “dianeutral diffusion” or “vertical diffusion.” This realization also has implications for the diffusion tensor.

Corresponding author address: Trevor J. McDougall, School of Mathematics and Statistics, University of New South Wales, NSW 2052, Australia. E-mail: trevor.mcdougall@unsw.edu.au
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