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.
Original language | English (US) |
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Pages (from-to) | 56-62 |
Number of pages | 7 |
Journal | Ocean Modelling |
Volume | 126 |
DOIs | |
State | Published - Jun 2018 |
Keywords
- Deformation
- Eddy parameterization
- LANS-α
- Mesoscale
- Non-Newtonian fluid
ASJC Scopus subject areas
- Computer Science (miscellaneous)
- Oceanography
- Geotechnical Engineering and Engineering Geology
- Atmospheric Science