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

Journal article

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.

Authors: Bachman, S; Anstey, J; Zanna, L

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Elsevier
• Journal: Ocean Modelling
• Volume: 126
• Pages: 56-62
• Publication date: 2018-04-27
• Acceptance date: 2018-04-25
• DOI: 10.1016/j.ocemod.2018.04.007
• EISSN: 1463-5011
• ISSN: 1463-5003
• Keywords: deformation; non-Newtonian fluid; LANS-α; eddy parameterization; mesoscale