2017/05/13 by Richard Blender, Gualtiero Badin · 1 citation
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Classical mechanics #Coastal and Marine Dynamics #Conservation law #Conservation of energy #Conserved quantity #Enstrophy #Flow (mathematics) #Geometry #Geostrophic wind #Hamiltonian (control theory) #Hamiltonian mechanics #Kinematic wave #Mathematical analysis #Mathematical optimization #Mathematical physics #Mathematics #Mechanics #Nonlinear Waves and Solitons #Numerical methods for differential equations #Ocean Waves and Remote Sensing #Physics #Poisson bracket #Potential vorticity #Quantum mechanics #Shallow water equations #Tropical and Extratropical Cyclones Research #Vortex #Vorticity
paper · pdf · doi:10.3390/fluids2020024
openalex publication_date 2017/05/13 · openalex created_date 2022/10/02 · openalex updated_date 2026/08/05
A systematic method to derive the Hamiltonian and Nambu form for the shallow water equations using the conservation for energy and potential enstrophy is presented. Different mechanisms, such as vortical flows and emission of gravity waves, emerge from different conservation laws for total energy and potential enstrophy. The equations are constructed using exterior differential forms and self-adjoint operators, and result in the sum of two Nambu brackets—one for the vortical flow and one for the wave-mean flow interaction—and a Poisson bracket representing the interaction between divergence and geostrophic imbalance. The advantage of this approach is that the Hamiltonian and Nambu forms can here be written in a coordinate-independent form.