Hamiltonian fluid mechanics
Irrotational barotropic flow
and the Hamiltonian by:
where e is the internal energy density, as a function of ρ. For this barotropic flow, the internal energy is related to the pressure p by:
where an apostrophe ('), denotes differentiation with respect to ρ.
This Hamiltonian structure gives rise to the following two equations of motion:
after exploiting the fact that the vorticity is zero:
- R. Salmon (1988). "Hamiltonian Fluid Mechanics". Annual Review of Fluid Mechanics 20: 225–256. Bibcode:1988AnRFM..20..225S. doi:10.1146/annurev.fl.20.010188.001301.
- T. G. Shepherd (1990). "Symmetries, conservation laws, and Hamiltonian structure in geophysical fluid dynamics". Advances in Geophysics 32: 287–338. Bibcode:1990AdGeo..32..287S. doi:10.1016/S0065-2687(08)60429-X.