The relationship between a deformation-based eddy parameterization and the LANS-α turbulence model. (June 2018)

• Record Type: Journal Article
• Authors: Bachman, Scott D.; Anstey, James A.; Zanna, Laure
• Is Part Of: Ocean modelling. Volume 126(2018)
• Page Start: 56
• Page End: 62
• Publication Date: 2018-06
• Subjects: Eddy parameterization -- Deformation -- LANS-α -- Mesoscale -- Non-Newtonian fluid; Oceanography -- Periodicals; Océanographie -- Périodiques; Oceanography; Periodicals; 551.46
• DOI: 10.1016/j.ocemod.2018.04.007
• Languages: English
• ISSNs: 1463-5003

Abstract

Highlights: The momentum closure in Anstey and Zanna (AZ, 2017) is extended and generalized to 3D. The momentum equations for a second-grade non-Newtonian fluid are nearly identical to LANS- α . Because AZ is based on the second-grade fluid equations, it is very similar to LANS- α . These similarities allow physical insights into one closure to be used to understand the other. Numerical techniques for implementing one model can be used for the other as well. Abstract: 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.