Zonally propagating wave solutions of Laplace Tidal Equations in a
                        baroclinic ocean of an aqua-planet

De-Leon, Yair; Paldor, Nathan

doi:10.1111/j.1600-0870.2010.00490.x

Cited by 23 publications

(19 citation statements)

References 9 publications

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“…As discussed in De‐Leon and Paldor (), the low energy‐states of the generic Schrödinger equation correspond to equatorially trapped waves, the latitude‐dependent amplitudes of which become negligible outside a narrow equatorial band. In particular, for n = 0 we consider the leading (second) order terms in the expansion of the potential on the left‐hand side of the generic Schrödinger equation in a power series in ϕ around the equator.…”

Section: A Complementary Perspective On the Mrg Wave Mode From A Schrmentioning

confidence: 92%

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The mixed Rossby–gravity wave on the spherical Earth

Paldor

Fouxon

Shamir

et al. 2018

Quart J Royal Meteoro Soc

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This work revisits the theory of the mixed Rossby–gravity (MRG) wave on a sphere. Three analytic methods are employed in this study: (a) derivation of a simple ad hoc solution corresponding to the MRG wave that reproduces the solutions of Longuet‐Higgins and Matsuno in the limits of zero and infinite Lamb's parameter, respectively, while remaining accurate for moderate values of Lamb's parameter, (b) demonstration that westward‐propagating waves with phase speed equalling the negative of the gravity‐wave speed exist, unlike the equatorial β‐plane, where the zonal velocity associated with such waves is infinite, and (c) approximation of the governing second‐order system by Schrödinger eigenvalue equations, which show that the MRG wave corresponds to the branch of the ground‐state solutions that connects Rossby waves with zonally symmetric waves. The analytic conclusions are confirmed by comparing them with numerical solutions of the associated second‐order equation for zonally propagating waves of the shallow‐water equations. We find that the asymptotic solutions obtained by Longuet‐Higgins in the limit of infinite Lamb's parameter are not suitable for describing the MRG wave even when Lamb's parameter equals 104. On the other hand, the dispersion relation obtained by Matsuno for the MRG wave on the equatorial β‐plane is accurate for values of Lamb's parameter as small as 16, even though the equatorial β‐plane formally provides an asymptotic limit of the equations on the sphere only in the limit of infinite Lamb's parameter.

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Section: A Complementary Perspective On the Mrg Wave Mode From A Schrmentioning

confidence: 92%

“…A similar Schrödinger description of the LSWEs on a sphere was developed in De‐Leon and Paldor () and Paldor et al. s*().…”

Section: Introductionmentioning

confidence: 99%

The mixed Rossby–gravity wave on the spherical Earth

Paldor

Fouxon

Shamir

et al. 2018

Quart J Royal Meteoro Soc

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“…As for the more cumbersome Trapped wave solution following De-Leon and Paldor (2011), and as was shown in Chaps. 4 and 5 when η is eliminated from (4.4), ψ and U 2 are given by:…”

Section: Planetary and Inertia-gravity Waves In A Mid-latitude Channementioning

confidence: 86%

Shallow Water Waves on the Rotating Earth

Paldor¹

2015

SpringerBriefs in Earth System Sciences

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“…Recently, Schrödinger eigenvalue problems were formulated for zonally propagating wave solutions of the LRSWE in midlatitudes (Paldor et al, 2007;Paldor and Sigalov, 2008) and approximate Schrödinger eigenvalue problems were also formulated on a sphere (De-Leon and Paldor, 2011;Paldor et al, 2013;Paldor, 2015). These formulations provide a clear and concise way of identifying the various waves and modes that solve the LRSWE.…”

Section: Introductionmentioning

confidence: 99%

Classification of eastward propagating waves on the spherical Earth

Garfinkel

Fouxon

Shamir

et al. 2017

Quart J Royal Meteoro Soc

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Observational evidence for an equatorial non-dispersive mode propagating at the speed of gravity waves is strong, and while the structure and dispersion relation of such a mode can be accurately described by a wave theory on the equatorial β-plane, prior theories on the sphere were unable to find such a mode except for particular asymptotic limits of gravity wave phase speeds and/or certain zonal wave numbers. Here, an ad hoc solution of the linearized rotating shallow-water equations (LRSWE) on a sphere is developed, which propagates eastward with phase speed that nearly equals the speed of gravity waves at all zonal wave numbers. The physical interpretation of this mode in the context of other modes that solve the LRSWE is clarified through numerical calculations and through eigenvalue analysis of a Schrödinger eigenvalue equation that approximates the LRSWE. By comparing the meridional amplitude structure and phase speed of the ad hoc mode with those of the lowest gravity mode on a non-rotating sphere we show that at large zonal wave number the former is a rotation-modified counterpart of the latter. We also find that the dispersion relation of the ad hoc mode is identical to the n = 0 eastward propagating inertia-gravity (EIG0) wave on a rotating sphere which is also nearly non-dispersive, so this solution could be classified as both a Kelvin wave and as the EIG0 wave. This is in contrast to Cartesian coordinates where Kelvin waves are a distinct wave solution that supplements the EIG0 mode. Furthermore, the eigenvalue equation for the meridional velocity on the β-plane can be formally derived as an asymptotic limit (for small (Lamb Number) -1/4 ) of the corresponding second order equation on a sphere, but this expansion is invalid when the phase speed equals that of gravity waves i.e. for Kelvin waves. Various expressions found in the literature for both Kelvin waves and inertia-gravity waves and which are valid only in certain asymptotic limits (e.g. slow and fast rotation) are compared with the expressions found here for the two wave types.

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Zonally propagating wave solutions of Laplace Tidal Equations in a baroclinic ocean of an aqua-planet

Cited by 23 publications

References 9 publications

The mixed Rossby–gravity wave on the spherical Earth

The mixed Rossby–gravity wave on the spherical Earth

Shallow Water Waves on the Rotating Earth

Classification of eastward propagating waves on the spherical Earth

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