Spurious Diapycnal Mixing Associated with Advection in a z-Coordinate Ocean Model

Stephen M. Griffies NOAA/Geophysical Fluid Dynamics Laboratory, Princeton, New Jersey

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Ronald C. Pacanowski NOAA/Geophysical Fluid Dynamics Laboratory, Princeton, New Jersey

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Robert W. Hallberg NOAA/Geophysical Fluid Dynamics Laboratory, Princeton, New Jersey

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Abstract

This paper discusses spurious diapycnal mixing associated with the transport of density in a z-coordinate ocean model. A general method, based on the work of Winters and collaborators, is employed for empirically diagnosing an effective diapycnal diffusivity corresponding to any numerical transport process. This method is then used to quantify the spurious mixing engendered by various numerical representations of advection. Both coarse and fine resolution examples are provided that illustrate the importance of adequately resolving the admitted scales of motion in order to maintain a small amount of mixing consistent with that measured within the ocean’s pycnocline. Such resolution depends on details of the advection scheme, momentum and tracer dissipation, and grid resolution. Vertical transport processes, such as convective adjustment, act as yet another means to increase the spurious mixing introduced by dispersive errors from numerical advective fluxes.

Corresponding author address: Dr. S. Griffies, Geophysical Fluid Dynamics Laboratory, Route 1, P.O. Box 308, Forrestal Campus, Princeton, NJ 08542.

Email: smg@gfdl.gov

Abstract

This paper discusses spurious diapycnal mixing associated with the transport of density in a z-coordinate ocean model. A general method, based on the work of Winters and collaborators, is employed for empirically diagnosing an effective diapycnal diffusivity corresponding to any numerical transport process. This method is then used to quantify the spurious mixing engendered by various numerical representations of advection. Both coarse and fine resolution examples are provided that illustrate the importance of adequately resolving the admitted scales of motion in order to maintain a small amount of mixing consistent with that measured within the ocean’s pycnocline. Such resolution depends on details of the advection scheme, momentum and tracer dissipation, and grid resolution. Vertical transport processes, such as convective adjustment, act as yet another means to increase the spurious mixing introduced by dispersive errors from numerical advective fluxes.

Corresponding author address: Dr. S. Griffies, Geophysical Fluid Dynamics Laboratory, Route 1, P.O. Box 308, Forrestal Campus, Princeton, NJ 08542.

Email: smg@gfdl.gov

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