Self-Consistent Finite-Mode Approximations for the Hydrodynamics of an Incompressible Fluid on Nonrotating and Rotating Spheres

Self-consistent finite-mode approximations for both Euler and Navier-Stokes equations for vorticity on a sphere are constructed and extended to the case of a rotating sphere, aiming at application to ocean and atmosphere modeling. In the absence of dissipation they preserve the specific Hamiltonian structure of hydrodynamics and have, at each level of approximation, an appropriate number of integrals of motion, which is not the case for standard schemes.