The relationship between a deformation-based eddy parameterization and the LANS-α turbulence model

Scott D. Bachman, James A. Anstey, Laure Zanna

Research output: Contribution to journalArticle


A recent class of ocean eddy parameterizations proposed by Porta Mana and Zanna (2014) and Anstey and Zanna (2017) modeled the large-scale flow as a non-Newtonian fluid whose subgridscale eddy stress is a nonlinear function of the deformation. This idea, while largely new to ocean modeling, has a history in turbulence modeling dating at least back to Rivlin (1957). The new class of parameterizations results in equations that resemble the Lagrangian-averaged Navier–Stokes-α model (LANS-α e.g., Holm et al., 1998a). In this note we employ basic tensor mathematics to highlight the similarities between these turbulence models using component-free notation. We extend the Anstey and Zanna (2017) parameterization, which was originally presented in 2D, to 3D, and derive variants of this closure that arise when the full non-Newtonian stress tensor is used. Despite the mathematical similarities between the non-Newtonian and LANS-α models which might provide insight into numerical implementation, the input and dissipation of kinetic energy between these two turbulent models differ.

Original languageEnglish (US)
Pages (from-to)56-62
Number of pages7
JournalOcean Modelling
StatePublished - Jun 2018



  • Deformation
  • Eddy parameterization
  • LANS-α
  • Mesoscale
  • Non-Newtonian fluid

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Oceanography
  • Geotechnical Engineering and Engineering Geology
  • Atmospheric Science

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