Momentum, Vorticity and Transport: Considerations in the Design of a Finite-Volume Dynamical Core

Ringler, Todd D.

doi:10.1007/978-3-642-11640-7_7

Cited by 5 publications

(4 citation statements)

References 21 publications

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“…Sorting through these details forms the content of finite volume methods used in computational fluid dynamics. For examples focused on oceanographic problems, see Adcroft et al (1997), Adcroft et al (2008), Ringler (2011), andAdcroft (2013). Importantly, all methods must respect the conservation Eq.…”

Section: Appendix F: Finite Volume Scalar Equationsmentioning

confidence: 99%

OMIP contribution to CMIP6: experimental and diagnostic protocol for the physical component of the Ocean Model Intercomparison Project

et al. 2016

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Abstract. The Ocean Model Intercomparison Project (OMIP) is an endorsed project in the Coupled Model Intercomparison Project Phase 6 (CMIP6). OMIP addresses CMIP6 science questions, investigating the origins and consequences of systematic model biases. It does so by providing a framework for evaluating (including assessment of systematic biases), understanding, and improving ocean, sea-ice, tracer, and biogeochemical components of climate and earth system models contributing to CMIP6. Among the WCRP Grand Challenges in climate science (GCs), OMIP primarily contributes to the regional sea level change and near-term (climate/decadal) prediction GCs.OMIP provides (a) an experimental protocol for global ocean/sea-ice models run with a prescribed atmospheric forcing; and (b) a protocol for ocean diagnostics to be saved as part of CMIP6. We focus here on the physical component of OMIP, with a companion paper (Orr et al., 2016) detailing methods for the inert chemistry and interactive biogeochemistry. The physical portion of the OMIP experimental protocol follows the interannual Coordinated Ocean-ice Reference Experiments (CORE-II). Since 2009, CORE-I (Normal Year Forcing) and CORE-II (Interannual Forcing) have become the standard methods to evaluate global ocean/sea-ice simulations and to examine mechanisms for forced ocean climate variability. The OMIP diagnostic protocol is relevant for any ocean model component of CMIP6, including the DECK (Diagnostic, Evaluation and Characterization of Klima experiments), historical simulations, FAFMIP (Flux Anomaly Forced MIP), C4MIP (Coupled Carbon Cycle Climate MIP), DAMIP (Detection and Attribution MIP), DCPP (Decadal Climate Prediction Project), ScenarioMIP, HighResMIP (High Resolution MIP), as well as the ocean/sea-ice OMIP simulations.

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Section: Appendix F: Finite Volume Scalar Equationsmentioning

confidence: 99%

OMIP contribution to CMIP6: experimental and diagnostic protocol for the physical component of the Ocean Model Intercomparison Project

et al. 2016

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“…However, differential equations do not provide our desired starting point for a finite volume formulation of discrete ocean model equations. We instead formulate integral budget equations for arbitrary closed moving fluid regions of finite extent, with our presentation inspired by similar treatments given by Donea et al (2004) and Ringler (2011). The resulting finite volume budgets for scalars (e.g., seawater mass, tracer mass, and potential enthalpy) and vectors (e.g., linear momentum and vorticity) offer a weak formulation of the ocean fluid mechanical equations, whereas the corresponding partial differential equations provide a strong formulation .…”

Section: Finite Volume Equations For Moving Fluid Regionsmentioning

confidence: 99%

A Primer on the Vertical Lagrangian‐Remap Method in Ocean Models Based on Finite Volume Generalized Vertical Coordinates

Griffies

Adcroft

Hallberg

2020

J Adv Model Earth Syst

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This paper provides a primer on the mathematical, physical, and numerical foundations of ocean models that are formulated using finite volume generalized vertical coordinate equations and that use the vertical Lagrangian-remap method to evolve the ocean state. We consider the mathematical structure of the governing ocean equations in both their strong formulation (partial differential equations) and weak formulation (finite volume integral equations), thus enabling an understanding of their physical content and providing a physical-mathematical framework to develop numerical algorithms. A connection is made between the Lagrangian-remap method and the ocean equations as written using finite volume generalized vertical budgets. Thought experiments are offered to exemplify the mechanics of the vertical Lagrangian-remap method and to compare with other methods used for ocean model algorithms. Plain Language Summary Numerical ocean models are based on a variety of mathematical methods that provide the framework for developing computational algorithms suitable for solving the ocean equations on a computer. The vertical Lagrangian-remap method is ideally suited for finite volume ocean models formulated using generalized vertical coordinates. It is gaining popularity among the ocean modeling community since it holds the potential to resolve longstanding limitations inherent with standard methods. However, there is some mystery surrounding the fundamentals of such ocean models. The goal of this paper is to dispel the mystery. We do so by providing a pedagogical treatment of the fluid mechanics that forms the basis for numerical ocean models formulated with finite volume generalized vertical coordinate equations and that use the vertical Lagrangian-remap method.

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“…Research. Numerous cores have been developed within the MPAS framework, including a shallow-water model (Ringler 2011), a hydrostatic atmosphere model (Rauscher et al 2013), a non-hydrostatic atmosphere model (Skamarock et al 2012), a hydrostatic ocean model (Ringler et al 2013), and sea-ice and land-ice models (under development).…”

Section: About the Model: Mpas-oceanmentioning

confidence: 99%

A study of overflow simulations using MPAS-Ocean: Vertical grids, resolution, and viscosity

2015

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MPAS-Ocean is used to simulate an idealized, density-driven overflow using the dynamics of overflow mixing and entrainment (DOME) setup. Numerical simulations are carried out using three of the vertical coordinate types available in MPAS-Ocean, including z-star with partial bottom cells, z-star with full cells, and sigma coordinates. The results are first benchmarked against other models, including the MITgcm's z-coordinate model and HIM's isopycnal coordinate model, which are used to set the base case used for this work. A full parameter study is presented that looks at how sensitive overflow simulations are to vertical grid type, resolution, and viscosity. Horizontal resolutions with 50 km grid cells are under-resolved and produce poor results, regardless of other parameter settings. Vertical grids ranging in thickness from 15 m to 120 m were tested. A horizontal resolution of 10 km and a vertical resolution of 60 m are sufficient to resolve the mesoscale dynamics of the DOME configuration, which mimics real-world overflow parameters. Mixing and final buoyancy are least sensitive to horizontal viscosity, but strongly sensitive to vertical viscosity. This suggests that vertical viscosity could be adjusted in overflow water formation regions to influence mixing and product water characteristics. Lastly, the study shows that sigma coordinates produce much less mixing than z-type coordinates, resulting in heavier plumes that go further down slope. Sigma coordinate are less sensitive to changes in resolution but as sensitive to vertical viscosity compared to z-coordinates.

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Momentum, Vorticity and Transport: Considerations in the Design of a Finite-Volume Dynamical Core

Cited by 5 publications

References 21 publications

OMIP contribution to CMIP6: experimental and diagnostic protocol for the physical component of the Ocean Model Intercomparison Project

OMIP contribution to CMIP6: experimental and diagnostic protocol for the physical component of the Ocean Model Intercomparison Project

A Primer on the Vertical Lagrangian‐Remap Method in Ocean Models Based on Finite Volume Generalized Vertical Coordinates

A study of overflow simulations using MPAS-Ocean: Vertical grids, resolution, and viscosity

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