Editorial Type:
Article
Article Type:
Research Article

Parameterization of Mixed Layer Eddies. Part I: Theory and Diagnosis

Baylor Fox-Kemper Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts

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Raffaele Ferrari Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts

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

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Print Publication:
01 Jun 2008
DOI:
https://doi.org/10.1175/2007JPO3792.1
Page(s):
1145–1165
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Abstract

Ageostrophic baroclinic instabilities develop within the surface mixed layer of the ocean at horizontal fronts and efficiently restratify the upper ocean. In this paper a parameterization for the restratification driven by finite-amplitude baroclinic instabilities of the mixed layer is proposed in terms of an overturning streamfunction that tilts isopycnals from the vertical to the horizontal. The streamfunction is proportional to the product of the horizontal density gradient, the mixed layer depth squared, and the inertial period. Hence restratification proceeds faster at strong fronts in deep mixed layers with a weak latitude dependence. In this paper the parameterization is theoretically motivated, confirmed to perform well for a wide range of mixed layer depths, rotation rates, and vertical and horizontal stratifications. It is shown to be superior to alternative extant parameterizations of baroclinic instability for the problem of mixed layer restratification. Two companion papers discuss the numerical implementation and the climate impacts of this parameterization.

* Current affiliation: Cooperative Institute for Research in the Environmental Sciences, and Department of Atmospheric and Oceanic Sciences, University of Colorado, Boulder, Colorado

Corresponding author address: Baylor Fox-Kemper, CIRES, and Department of Atmospheric and Oceanic Sciences, University of Colorado, Boulder, CO 80309. bfk@colorado.edu

Abstract

Ageostrophic baroclinic instabilities develop within the surface mixed layer of the ocean at horizontal fronts and efficiently restratify the upper ocean. In this paper a parameterization for the restratification driven by finite-amplitude baroclinic instabilities of the mixed layer is proposed in terms of an overturning streamfunction that tilts isopycnals from the vertical to the horizontal. The streamfunction is proportional to the product of the horizontal density gradient, the mixed layer depth squared, and the inertial period. Hence restratification proceeds faster at strong fronts in deep mixed layers with a weak latitude dependence. In this paper the parameterization is theoretically motivated, confirmed to perform well for a wide range of mixed layer depths, rotation rates, and vertical and horizontal stratifications. It is shown to be superior to alternative extant parameterizations of baroclinic instability for the problem of mixed layer restratification. Two companion papers discuss the numerical implementation and the climate impacts of this parameterization.

* Current affiliation: Cooperative Institute for Research in the Environmental Sciences, and Department of Atmospheric and Oceanic Sciences, University of Colorado, Boulder, Colorado

Corresponding author address: Baylor Fox-Kemper, CIRES, and Department of Atmospheric and Oceanic Sciences, University of Colorado, Boulder, CO 80309. bfk@colorado.edu

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