Stable and Unstable Eigensolutions of Laplace’s Tidal Equations for Zonal Wavenumber Zero

Rolf Müller

doi:10.1007/BF02656951

Impact Factor: 5.8

Volume 10 Issue 1

Jan. 1993

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Article > ADVANCES IN ATMOSPHERIC SCIENCES > 1993 > 10(1): 21-40

Stable and Unstable Eigensolutions of Laplace’s Tidal Equations for Zonal Wavenumber Zero

Rolf Müller

1.
Max-Planck-Institut fur Chemie Abt. Luftchemie Postfach 3060 D-6500 Mainz, FRG

Rolf Müller

doi: 10.1007/BF02656951

Abstract
References
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Abstract:
Laplace's tidal equations are of great importance in various fields of geophysics. Here, the special case of zonal symmetry (zonal wavenumber m = 0) is investigated, where degenerate sets of eigensolutions appear. New results are presented for the inclusion of dissipative processes and the case of unstable conditions. In both instances the (nonzero) eigenfrequencies are complex. In the latter case, additional stable (i.e. real) eigenfrequencies appear in the numerical results for the absolute value of the Lambparameter ε being larger than a critical value εc. Further, it is shown that any degeneracies are removed through the inclusion of dissipation. Moreover, asymptotic relations are derived employing the relation of Laplace's tidal equations for m = 0 to the spheroidal differential equation. The implications of these findings to numerical techniques are demonstrated and results of computations are presented.
References

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Manuscript History

Manuscript received: 10 January 1993

Manuscript revised: 10 January 1993

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Stable and Unstable Eigensolutions of Laplace’s Tidal Equations for Zonal Wavenumber Zero

Rolf Müller

1. Max-Planck-Institut fur Chemie Abt. Luftchemie Postfach 3060 D-6500 Mainz, FRG

Manuscript received: 1993-01-10
Manuscript revised: 1993-01-10

Abstract: Laplace's tidal equations are of great importance in various fields of geophysics. Here, the special case of zonal symmetry (zonal wavenumber m = 0) is investigated, where degenerate sets of eigensolutions appear. New results are presented for the inclusion of dissipative processes and the case of unstable conditions. In both instances the (nonzero) eigenfrequencies are complex. In the latter case, additional stable (i.e. real) eigenfrequencies appear in the numerical results for the absolute value of the Lambparameter ε being larger than a critical value εc. Further, it is shown that any degeneracies are removed through the inclusion of dissipation. Moreover, asymptotic relations are derived employing the relation of Laplace's tidal equations for m = 0 to the spheroidal differential equation. The implications of these findings to numerical techniques are demonstrated and results of computations are presented.