Multi-Scale Localized Perturbation Method for Geophysical Fluid Flows

An alternative formulation of the governing equations of a dynamical system, called the multi-scale localized perturbation method, is introduced and derived for the purpose of solving complex geophysical flow problems. Simulation variables are decomposed into background and perturbation components, then assumptions are made about the evolution of these components within the context of an environmental flow in order to close the system. Once closed, the original governing equations become a set of one-way coupled governing equations called the "delta form" of the governing equations for short, with one equation describing the evolution of the background component and the other describing the evolution of the perturbation component. One-way interaction which arises due to non-linearity in the original differential equations appears in this second equation, allowing the background fields to influence the evolution of a perturbation. Several solution methods for this system of equations are then proposed. Advantages of the delta form include the ability to specify a complex, temporally- and spatially-varying background field separate from a perturbation introduced into the system, including those created by natural or man-made sources, which enhances visualization of the perturbation as it evolves in time and space. The delta form is also shown to be a tool which can be used to simplify simulation setup. Implementation of the delta form of the incompressible URANS equations with turbulence model and scalar transport within OpenFOAM is then documented, followed by verification cases. A stratified wake collapse case in a domain containing a background shear layer is then presented, showing how complex internal gravity wave-shear layer interactions are retained and easily observed in spite of the variable decomposition. The multi-scale localized perturbation method shows promise for geophysical flow problems, particularly multi-scale simulation involving the interaction of large-scale natural flows with small-scale flows generated by man-made structures.