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A perturbation approach to understanding the effects of turbulence on frontogenesis

Published online by Cambridge University Press:  25 November 2019

Abigail S. Bodner Open the ORCID record for Abigail S. Bodner [Opens in a new window] ,
Baylor Fox-Kemper Open the ORCID record for Baylor Fox-Kemper [Opens in a new window] ,
Luke P. Van Roekel Open the ORCID record for Luke P. Van Roekel [Opens in a new window] ,
James C. McWilliams Open the ORCID record for James C. McWilliams [Opens in a new window]  and
Peter P. Sullivan Open the ORCID record for Peter P. Sullivan [Opens in a new window]
Abigail S. Bodner*
Affiliation:
Department of Earth, Environmental and Planetary Sciences, Brown University, Providence,RI02912, USA
Baylor Fox-Kemper
Affiliation:
Department of Earth, Environmental and Planetary Sciences, Brown University, Providence,RI02912, USA
Luke P. Van Roekel
Affiliation:
Theoretical Division, Fluid Dynamics and Solid Mechanics, Los Alamos National Laboratory, Los Alamos, NM87545, USA
James C. McWilliams
Affiliation:
Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles,CA90095-1565, USA
Peter P. Sullivan
Affiliation:
National Center for Atmospheric Research, Boulder, CO80307-3000, USA
*
†Email address for correspondence: abigail_bodner@brown.edu
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Abstract

Ocean fronts are an important submesoscale feature, yet frontogenesis theory often neglects turbulence – even parameterized turbulence – leaving theory lacking in comparison with observations and models. A perturbation analysis is used to include the effects of eddy viscosity and diffusivity as a first-order correction to existing strain-induced inviscid, adiabatic frontogenesis theory. A modified solution is obtained by using potential vorticity and surface conditions to quantify turbulent fluxes. It is found that horizontal viscosity and diffusivity tend to be readily frontolytic – reducing frontal tendency to negative values under weakly non-conservative perturbations and opposing or reversing front sharpening, whereas vertical viscosity and diffusivity tend to only weaken frontogenesis by slowing the rate of sharpening of the front even under strong perturbations. During late frontogenesis, vertical diffusivity enhances the rate of frontogenesis, although perturbation theory may be inaccurate at this stage. Surface quasi-geostrophic theory – neglecting all injected interior potential vorticity – is able to describe the first-order correction to the along-front velocity and ageostrophic overturning circulation in most cases. Furthermore, local conditions near the front maximum are sufficient to reconstruct the modified solution of both these fields.

JFM classification

Mixing: Turbulent mixing Geophysical and Geological Flows: Ocean processes Geophysical and Geological Flows: Quasi-geostrophic flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 883 , 25 January 2020 , A25
Copyright
© 2019 Cambridge University Press

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