Construction of Hamiltonian and Nambu Forms for the Shallow Water Equations
Abstract
:1. Introduction
2. The Shallow Water Equations
3. Construction of the Dynamical Equations
3.1. Vorticity Advection
3.2. Gravity Waves
3.3. Vortical Component of the Flow and Gravity Waves Interaction
3.4. Noncanonical Hamiltonian Form of the Equations
4. Nambu and Poisson brackets
4.1. Vorticity Equation
4.2. Gravity Waves
4.3. Vorticity-Potential Flow Interaction
5. Summary
Acknowledgments
Author Contributions
Conflicts of Interest
Appendix A. Nambu form of a Finite Dimensional Fast-Slow Shallow Water System
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Blender, R.; Badin, G. Construction of Hamiltonian and Nambu Forms for the Shallow Water Equations. Fluids 2017, 2, 24. https://doi.org/10.3390/fluids2020024
Blender R, Badin G. Construction of Hamiltonian and Nambu Forms for the Shallow Water Equations. Fluids. 2017; 2(2):24. https://doi.org/10.3390/fluids2020024
Chicago/Turabian StyleBlender, Richard, and Gualtiero Badin. 2017. "Construction of Hamiltonian and Nambu Forms for the Shallow Water Equations" Fluids 2, no. 2: 24. https://doi.org/10.3390/fluids2020024