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High-Order Multi-Resolution Multi-Dynamics Modeling for the

Flow Encountering Abrupt Topography (FLEAT) Initiative

P.F.J. Lermusiaux, P.J. Haley, Jr.,
C. Mirabito

Massachusetts Institute of Technology
Ocean Science and Engineering
Mechanical Engineering
Cambridge, Massachusetts

Project Summary
Ongoing MIT-MSEAS Research
Additional FLEAT Links
Background Information
References

 

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This research is sponsored by the Office of Naval Research.

Project Summary

The presence of large gradients often renders the quantitative analysis of dynamical systems challenging, be the analysis theoretical, observational or computational. This is because large gradients commonly lead to strong nonlinearities and to coupling among state variables and parameters. The emphasis of the Flow Encountering Abrupt Topography (FLEAT) initiative is on the effects of large topographic gradients and complex subsurface geometry on major current systems. First, the processes involved in these strong topographic interactions are not yet well known. Their consequences, including alteration of circulation features, spawning of internal waves and vortices, and formation of unstable downslope flows and gravity currents, require novel integrated analyses. Second, major ocean ridges and archipelagos and islands are not properly represented in larger-scale modeling systems, and novel downscaling and two-way nesting schemes need to be utilized, developed and evaluated with real ocean data. This set of research activities is the emphasis of our FLEAT research project.

Background information is available below.

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Ongoing MIT-MSEAS Research

Long-Term (Collaborative) Goal:

Explain and quantify multiscale interactions at abrupt topography among flow systems, vortices, internal tides and/or slope currents

  1. by using and developing high-order multi-dynamics Hybridizable Discontinuous Galerkin (HDG) schemes for accurate process studies, and
  2. by using and improving downscaling and two-way nesting schemes for realistic simulations and dynamics analyses.

Specific Objectives:

Presentations and Meetings

FLEAT-supported Publications

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Additional FLEAT Links

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Background Information

In collaboration with the DRI team, one of our motivations is to quantify processes involved when flows encounter abrupt topographic gradients with complex subsurface features and island chains, with an emphasis on multiscale interactions that occur in the west Mariana Ridge region. A second motivation is to achieve accurate simulations that resolve locally strong gradients over dynamically significant space- and time-scales. To do so, high-order schemes (more accurate for the same efficiency than lower-order schemes) and multi-resolution meshes (allow optimized refinements) are desirable. All of this, as well as conservative and consistency considerations, led us to hybridizable discontinuous Galerkin (HDG) methods (Cockburn et al., 2009a; Nguyen et al, 2009a). Specifically, we derived new HDG schemes for high-order, multi-resolution modeling of incompressible fluid and Boussinesq ocean dynamics (Ueckermann and Lermusiaux, 2010; Ueckermann and Lermusiaux, 2015; Ueckermann et al., 2015; Mirabito et al., 2015). Some of the next research steps are to refine their implementations, study their numerical properties and enable high-order-accurate scientific studies of multi-dynamics interactions. Such interactions will occur in the FLEAT study regions and include circulations with non-hydrostatic and hydrostatic regions, or flows with both geostrophic and strongly ageostrophic motions. Our final motivation is to utilize our MSEAS multiscale modeling capabilities (Haley and Lermusiaux, 2010; Haley et al., 2015), including semi-analytical archipelago flow initialization, data assimilation, sensitivity and diagnostic studies, and Lagrangian analyses.

Specific Research Tasks

Quantitative process studies with high-order multi-resolution multi-dynamics modeling

In collaboration with the DRI team, we plan to explain and quantify multiscale interactions at abrupt topography. We will define and set-up flow configurations that encounter abrupt topographic gradients, with or without subsurface features and islands. This will involve time and 2D and 3D-in-space studies. To complete these studies, we will further develop our HDG codes towards a high fidelity modeling system, capable of multi-dynamics simulations at high-order over multi-resolution meshes. We plan to simulate and study nonlinear dynamics with non-hydrostatic or hydrostatic dynamics turned on. We plan to emphasize the multiscale interactions among the regional features observed, including non-hydrostatic stirring and mixing. We intend to utilize modeling and measurement results to inspire the development of process-oriented dynamical models for these interactions. We also plan to utilize our modeling results during the field campaigns to guide the sea sampling towards key processes and interactions.

Downscaling and implicit two-way nesting of multiple dynamics in complex geometries

For realistic simulations and dynamics analyses in complex geometries, we will refine and utilize our nested-grid boundary conditions and conservative multi-grid exchanges such that upscale and downscale effects of multiple dynamics are transferred accurately across the multi-resolution domains. We also plan to utilize and further evaluate our semi-analytical optimization scheme for the estimation of circulation features in complex multiply-connected regions, generalizing the “Island Rule”. We will improve our generalized vertical coordinate systems for primitive-equations (PEs) with a nonlinear free-surface, implementing model levels that optimally adapt to dynamics, for both our structured finite-volume and unstructured HDG codes. Finally, we plan to implement our HDG solver capability of separating non-hydrostatic and hydrostatic elements.

Realistic data-assimilative multi-resolution modeling and dynamics analyses

We will set-up and apply our MSEAS PE code for multi-resolution modeling of multiscale tidal-to-mesoscale processes in the FLEAT regions. This involves two-way implicit nesting, parameter tuning, data assimilation, and data-model comparisons. We intend to explain and quantify processes involved when regional currents encounter the abrupt topography, subsurface features and island chains, with an emphasis on multiscale interactions. We plan to complete re-analyses with telescoping two-way nesting, to be used for dynamics analyses. For dynamics analyses, we plan to utilize term-by-term and flux balances, LCSs analyses, time and space variability decompositions, and/or new internal tide extraction equations that we developed.

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References

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Go to the MSEAS home page