Towards internal wave resolving simulations of the ocean
Abstract/Contents
- Abstract
- Most ocean models solve the hydrostatic primitive equations. Small-scale processes such as nonlinear internal solitary waves, however, require computationally expensive nonhydrostatic simulations to be well-resolved because the balance of nonlinearity and dispersion is responsible for the wave's shape. The main goal of this dissertation is to inform the practice of nonhydrostatic ocean modeling. To this end, I have examined the accuracy and stability of poplar methods used in nonhydrostatic modeling. Most ocean models are second-order accurate, inducing numerical dispersion generated from odd-order terms in the truncation error. Numerical dispersion is problematic because it mimics physical dispersion due to nonhydrostasy. To ensure relative dominance of physical over numerical effects, simulations require the horizontal grid spacing ([Delta] x) to be less than the depth of the internal interface (h1). When this condition is not satisfied, numerical dispersion overwhelms physical dispersion, and modeled internal waves exist with a dynamical balance between nonlinearity and numerical dispersion. Satisfaction of this condition may be a significant additional resolution requirement beyond the current state-of-the-art in ocean modeling. To cope with this high horizontal resolution requirement, it becomes necessary to find other means of reducing resolution requirements and computational cost. To this end, I suggest a specific framework which has been implemented as a prototype for a next-generation ocean model. The new model is a nonhydrostatic, isopycnal-coordinate ocean model, which to my knowledge is the first of its kind. Isopycnal coordinates provide a natural representation of the problem physics which in turn reduces the number of vertical grid points and thus improves efficiency. Existing isopycnal-coordinate models are purely hydrostatic owing to the nearly hydrostatic scaling of most oceanic processes and the belief that nonhydrostatic effects are only associated with overturning motions which cannot be represented in isopycnal coordinates. However, processes such as nonlinear internal solitary waves are clearly nonhydrostatic and not associated with overturning motions. Thus a nonhydrostatic isopycnal coordinate model may be well-suited to simulating nonlinear internal solitary waves. Ideally, when the internal wave structure is predominantly mode-1, an isopycnal model with only two layers may suffice. I demonstrate that the new model is capable of simulating a variety of nonhydrostatic processes in idealized test cases with a reduced number of vertical layers.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2013 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Vitousek, Sean |
|---|---|
| Associated with | Stanford University, Department of Civil and Environmental Engineering. |
| Primary advisor | Fringer, Oliver B. (Oliver Bartlett) |
| Thesis advisor | Fringer, Oliver B. (Oliver Bartlett) |
| Thesis advisor | Koseff, Jeffrey Russell |
| Thesis advisor | Monismith, Stephen Gene |
| Advisor | Koseff, Jeffrey Russell |
| Advisor | Monismith, Stephen Gene |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Sean Vitousek. |
|---|---|
| Note | Submitted to the Department of Civil and Environmental Engineering. |
| Thesis | Ph.D. Stanford University 2013 |
| Location | electronic resource |
Access conditions
- Copyright
- © 2013 by Sean Francis Keolu'aloha Vitousek
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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