@inproceedings{15005228eb754c53ab8d513da595428d,
title = "A unified linear wave theory of the Shallow Water Equations on a rotating plane",
abstract = "The linearized Shallow Water Equations (LSWE) on a tangent (x, y) plane to the rotating spherical Earth with Coriolis parameter f(y) that depends arbitrarily on the northward coordinate y is considered as a spectral problem of a selfadjoint operator. This operator is associated with a linear second-order equation in x - y plane that yields all the known exact and approximate solutions of the LSWE including those that arise from different boundary conditions, vanishing of some small terms (e.g. the β-term and frequency) and certain forms of the Coriolis parameter f(y) on the equator or in mid-latitudes. The operator formulation is used to show that all solutions of of the LSWE are stable. In some limiting cases these solutions reduce to the well-known plane waves of geophysical fluid dynamics: Inertia-gravity (Poincar{\'e}) waves, Planetary (Rossby) waves and Kelvin waves. In addition, the unified theory yields the non-harmonic analogs of these waves as well as the more general propagating solutions and solutions in closed basins.",
keywords = "Beta-plane, Closed basins, F-plane, Gravity waves",
author = "Nathan Paldor and Andrey Sigalov",
year = "2008",
doi = "10.1007/978-1-4020-6744-0_36",
language = "אנגלית",
isbn = "9781402067433",
series = "Solid Mechanics and its Applications",
publisher = "Springer Verlag",
pages = "403--413",
booktitle = "IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence - Proceedings of the IUTAM Symposium",
address = "גרמניה",
note = "IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence ; Conference date: 25-08-2006 Through 30-08-2006",
}