CMG Collaborative Research: Ocean Modeling by Bridging Primitive and Boussinesq Equations

Illinois Institute Of Technology, Chicago IL

Investigators

Abstract

While vast regions of the ocean can be treated accurately within the framework of eddy-resolving ocean models integrating simplified equations, there are comparatively small regions in which rapidly-evolving three dimensional motions are important not only for local but also for large-scale dynamics, thereby playing an important role in the multi-scale dynamics of both coastal and global oceanic flows. The flow dynamics in these small regions are complex enough not to permit an accurate approximation by simple parameterizations, but rather demand solution of the full set of equations. The objective of this project is to build a modeling framework which can handle both energetically active motions and large scale general circulations simultaneously. This research-education project is an orchestrated effort of a collaboration synthesizing expertise in both mathematics and oceanography. The blend of mathematical, computational, and geophysical expertise of the project team is central to the success of this endeavor. It is also essential to the truly interdisciplinary training of graduate and undergraduate students, who will be involved in all the stages of a research project: Modeling, mathematical analysis, discretization, validation, computation, and data analysis. To model these challenging oceanic flows, a truly multi-scale modeling framework that will employ the computationally intensive Boussinesq equations only in the small regions of intense mixing and the computationally efficient primitive equations in the rest of the fluid domain is needed. The inherent multi-scale nature of the oceanic flows considered, however, makes the development of such a modeling framework challenging, both mathematically and computationally. Indeed, one needs to address outstanding open questions, such as, the mathematical bridging of two different systems of equations, the interfacing of computational meshes of vastly varying resolutions, the quantification and modeling of uncertainty in this complex framework and the modeling of oceanic flows over a range of scales where forward and backward energy cascades coexist. This new framework comprises several significant mathematical and computational developments: (i) a new multiphysics/multiresolution modeling approach based on domain decomposition that will allow an appropriate treatment of highly varying mesh resolutions and the interfacing of the non-hydrostatic and hydrostatic flow regimes; (ii) a novel spatio-temporal filtering methodology that provides an elegant mathematical approach for bridging two different sets of equations by creating a spectrum of intermediate models filling the gap between the two sets of equations in terms of computational efficiency and physical accuracy; (iii) new modeling strategies for the uncertainty in the system generated by the inherently stochastic nature of the Boussinesq-primitive equations coupling; and (iv) state-of-the-art turbulence modeling for an appropriate treatment of the markedly different turbulence character of the Boussinesq and primitive flow regimes by taking advantage of the mathematical nature of approximate deconvolution approaches.