This monograph provides a concise overview of nonlinear internal wave theory. It serves as a self-contained reference for both students of mathematics as well as scientific professionals by presenting the material in two parts, isolating the narrative analysis from the mathematical detail. This unique format allows the text to remain accessible to oceanographers and researchers outside of mathematics by presenting a range of relevant theories on their own terms. Conversely, it enables applied mathematicians to understand how the conversation between mathematics and sciences proceeds in a field that has developed through a combination of the two. In addition, the text is supplemented by hands-on Matlab software, as the book incorporates a collection of working codes that enable readers to reproduce all theoretical figures in the text, with modification potential to fit a range of applications including a number of mini-projects outlined throughout the text.
Author(s): Marek Stastna
Series: Surveys and Tutorials in the Applied Mathematical Sciences, 9
Publisher: Springer
Year: 2022
Language: English
Pages: 128
City: Cham
Preface
Reader's Guide
Literature Preface
References
Contents
1 Background and Equation Summaries
Mathematics Background
Wave Theory Background
Fluid Mechanics Background
Stratified Fluid Mechanics Background
Equation Boxes
Literature 1
References
2 Derivations: Linear, Weakly Nonlinear, and Conjugate Flow Theory
The Taylor–Goldstein Equation
Non-dimensionalization
KdV Theory
The O(1) Problem
The O(ε) Problem
The O(μ) Problem
Commentary
Conjugate Flow Theory
Concluding Thoughts
Literature 2
References
3 Using Linear and Weakly Nonlinear Theory
Doing It Numerically Part I: Linear Theory
Doing It Numerically Part II: WNL
Concluding Thoughts
Literature 3
References
4 Exact Internal Solitary Waves
DJL Theory
Doing It Numerically Part III: DJL
Concluding Thoughts
Literature 4
References
5 Exact Internal Hydraulics
Steady DJL Theory
Steady DJL Numerics
Steady DJL Results
Open Problems and Mini-projects
Literature 5
References
6 Mode-2 Waves
Mode-2 Waves via Lock Release
Mode Diagnostics and Mode-1 Tails
Exotic Mode-2 Waves
Literature 6
References
7 Concluding Thoughts
Literature 7
References
Index
