Abstract
A modified set of governing differential equations for geophysical fluid flows is derived. All of the simulation fields are decomposed into a nominal large-scale background state and a small-scale perturbation from this background, and the new system is closed by the assumption that the perturbation is one-way coupled to the background. The decomposition method, termed the multi-scale localized perturbation method (MSLPM), is then applied to the governing equations of stratified fluid flows, implemented in OpenFOAM, and exercised in order to simulate the interaction of a vertically-varying background shear flow with an axisymmetric perturbation in a turbulent ocean environment. The results demonstrate that the MSLPM can be useful in visualizing the evolution of a perturbation within a complex background while retaining the complex physics that are associated with the original governing equations. The simulation setup may also be simplified under the MSLPM framework. Further applications of the MSLPM, especially to multi-scale simulations that encompass a large range of spatial and temporal scales, may be beneficial for researchers.
Highlights
Advancements in computational methods and hardware have enabled researchers and engineers to use computers in order to understand and model increasingly-complex phenomena
The aim of this work is to simulate the dynamics of a perturbation to a geophysical flow while using modified forms of the governing equations of stratified fluid dynamics
The ability to independently track the evolution of a perturbation within an evolving background is one of the most prominent benefits of the multi-scale localized perturbation method (MSLPM)
Summary
Advancements in computational methods and hardware have enabled researchers and engineers to use computers in order to understand and model increasingly-complex phenomena. Researchers have the ability to calculate, for example, not just the hydrodynamics of the Earth’s oceans over time, and the distribution of temperature, salinity, mixed-layer depth, and sea-ice thickness, and compare these quantities across different software and models [2]. The time and space resolution of a computational simulation limits the time- and length-scales, which may be resolved by any given simulation. When a wide range of scales must be resolved, computational resource limitations require that concessions be made in which scales receive adequate resolution, an example of this being turbulence modeling for modeling the smallest necessary scales
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