TY - JOUR

T1 - The eigenvalue equations of equatorial waves on a sphere

AU - De-Leon, Yair

AU - Erlick, Carynelisa

AU - Paldor, Nathan

PY - 2010/1

Y1 - 2010/1

N2 - Zonally propagating wave solutions of the linearized shallow water equations (LSWE) in a zonal channel on the rotating spherical earth are constructed from numerical solutions of eigenvalue equations that yield the meridional variation of the waves' amplitudes and the phase speeds of these waves. An approximate Schr̈odinger equation, whose potential depends on one parameter only, is derived, and this equation yields analytic expressions for the dispersion relations and for the meridional structure of the waves' amplitudes in two asymptotic cases. These analytic solutions validate the accuracy of the numerical solutions of the exact eigenvalue equation. Our results show the existence of Kelvin, Poincaŕe and Rossby waves that are harmonic for large radius of deformation. For small radius of deformation, the latter two waves vary as Hermite functions. In addition, our results show that the mixed mode of the planar theory (a meridional wavenumber zero mode that behaves as a Rossby wave for large zonal wavenumbers and as a Poincaŕe wave for small ones) does not exist on a sphere; instead, the first Rossby mode and the first westward propagating Poincaŕe mode are separated by the anti-Kelvin mode for all values of the zonal wavenumber.

AB - Zonally propagating wave solutions of the linearized shallow water equations (LSWE) in a zonal channel on the rotating spherical earth are constructed from numerical solutions of eigenvalue equations that yield the meridional variation of the waves' amplitudes and the phase speeds of these waves. An approximate Schr̈odinger equation, whose potential depends on one parameter only, is derived, and this equation yields analytic expressions for the dispersion relations and for the meridional structure of the waves' amplitudes in two asymptotic cases. These analytic solutions validate the accuracy of the numerical solutions of the exact eigenvalue equation. Our results show the existence of Kelvin, Poincaŕe and Rossby waves that are harmonic for large radius of deformation. For small radius of deformation, the latter two waves vary as Hermite functions. In addition, our results show that the mixed mode of the planar theory (a meridional wavenumber zero mode that behaves as a Rossby wave for large zonal wavenumbers and as a Poincaŕe wave for small ones) does not exist on a sphere; instead, the first Rossby mode and the first westward propagating Poincaŕe mode are separated by the anti-Kelvin mode for all values of the zonal wavenumber.

UR - http://www.scopus.com/inward/record.url?scp=77249117807&partnerID=8YFLogxK

U2 - 10.1111/j.1600-0870.2009.00420.x

DO - 10.1111/j.1600-0870.2009.00420.x

M3 - Article

AN - SCOPUS:77249117807

SN - 0280-6495

VL - 62

SP - 62

EP - 70

JO - Tellus, Series A: Dynamic Meteorology and Oceanography

JF - Tellus, Series A: Dynamic Meteorology and Oceanography

IS - 1

ER -