A unified linear wave theory of the Shallow Water Equations on a rotating plane

Nathan Paldor*, Andrey Sigalov

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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 (Poincaré) 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.

Original languageEnglish
Title of host publicationIUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence - Proceedings of the IUTAM Symposium
PublisherSpringer Verlag
Pages403-413
Number of pages11
ISBN (Print)9781402067433
DOIs
StatePublished - 2008
EventIUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence - Moscow, Russian Federation
Duration: 25 Aug 200630 Aug 2006

Publication series

NameSolid Mechanics and its Applications
Volume6
ISSN (Print)1875-3507

Conference

ConferenceIUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence
Country/TerritoryRussian Federation
CityMoscow
Period25/08/0630/08/06

Keywords

  • Beta-plane
  • Closed basins
  • F-plane
  • Gravity waves

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