Normal Modes of the Atlantic and Indian Oceans

Platzman, George W.

doi:10.1175/1520-0485(1975)005<0201:nmotaa>2.0.co;2

Cited by 59 publications

(30 citation statements)

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“…has been found to increase strongly the frequencies of the planetary basin modes in numerical models (Christensen (1973b) and Platzman (1975)) and analytical studies (Ripa (1978)). …”

Section: 6mentioning

confidence: 80%

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Observations of long period waves in the tropical oceans and atmosphere

Luther¹

1980

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“…has been found to increase strongly the frequencies of the planetary basin modes in numerical models (Christensen (1973b) and Platzman (1975)) and analytical studies (Ripa (1978)). …”

Section: 6mentioning

confidence: 80%

“…Although the scatter is large, westward propagation is clear. There is a suggestion that the wavelength is decreasing with latitude (see Table 3.10), but it is not useful to interpret the variations in term of existing constant-depth models because topography can be expected to alter the eigenfunctions significantly (Platzman (1975)). …”

Section: 6mentioning

confidence: 99%

Observations of long period waves in the tropical oceans and atmosphere

Luther¹

1980

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“…When meridional boundaries are taken into account, a discrete spectrum of modes arises, so-called Rossby basin modes (Longuet-Higgins 1964). Many studies have shown that bathymetry drastically affects the propagation characteristics of Rossby waves and basin modes (e.g., Rhines 1969; Anderson and Killworth 1977;Ripa 1978;Platzman 1975;Platzman et al 1981;Miller 1986;Miller et al 1987;Miller 1989). In fact, Koblinsky (1990) showed that there are relatively few places in the World Ocean where the planetary vorticity gradient ␤ 0 is the dominant component of the potential vorticity gradient.…”

Section: Discussionmentioning

confidence: 99%

Multiple Oscillatory Modes of the Argentine Basin. Part II: The Spectral Origin of Basin Modes

Weijer

Vivier

Gille

et al. 2007

Journal of Physical Oceanography

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In this paper the spectrum of barotropic basin modes of the Argentine Basin is shown to be connected to the classical Rossby basin modes of a flat-bottom (constant depth), rectangular basin. First, the spectrum of basin modes is calculated for the Argentine Basin, by performing a normal-mode analysis of the barotropic shallow-water equations. Then a homotopy transformation is performed that gradually morphs the full-bathymetry geometry through a flat-bottom configuration into a rectangular basin. Following the eigenmodes through this transition establishes a connection between most of the basin modes and the classical Rossby basin modes of a rectangular geometry. In particular, the 20-day mode of the Argentine Basin is identified with the lowest-order mode of classical theory. Sensitivity studies show that the decay rate of each mode is controlled by bottom friction, but that it is insensitive to lateral friction; lateral friction strongly impacts the oscillation frequency. In addition, the modes are found to be only slightly sensitive to the presence of a background flow.

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“…We give here error estimates for a finite element procedure proposed by Platzman [15] to approximate the spectral properties of (0.2). The self adjoint case / = 0 was analyzed by Luskin [11] by techniques different from those used here.…”

mentioning

confidence: 99%

“…With these spaces we associate the inner product and norms The functions {<b, ip} are known as Stokes-Helmholtz potentials for w [8], [15], and we define the functions Su = <b, Hu = tp. It follows from elliptic regularity [10] that for k > 0, there exists c = c(k), c < 00, such that We assume that there exists a positive constant c, independent of h, and a positive integer r such that, for 1 < k < r + 1 and w E 77*(ß), (4)(5)(6)(7)(8)(9) xèn4(l|w' ~x"+A||w "xl|i) < C/I*HI*'…”

mentioning

confidence: 99%

Approximation of the Spectrum of Closed Operators: The Determination of Normal Modes of a Rotating Basin

Descloux¹,

Luskin²,

Rappaz³

1981

Mathematics of Computation

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Abstract. This paper gives a theory of spectral approximation for closed operators in Banach spaces. The perturbation theory developed in this paper is applied to the study of a finite element procedure for approximating the spectral properties of a differential system modeling a fluid in a rotating basin.Introduction. In this paper, we give a theory of spectral approximation for closed operators in Banach spaces. We then apply this theory to an analysis of the approximation of the spectral properties of some differential systems by finite element methods.Bramble and Osborn [1] and Osborn [14] developed a theory of spectral approximation for compact operators in Banach spaces. Their theory can be applied to the analysis of many numerical procedures for the spectral approximation of differential operators, T, such that T + XI has a compact inverse for some X G C. Most of the differential systems in the theory of elasticity are in this class.However, there are many differential systems of interest in mathematical physics which do not have compact resolvents. These operators can have continuous spectrum, eigenvalues of infinite multiplicity, and finite limit points of eigenvalues. Also, the eigenfunctions need not be smooth since the differential systems are not necessarily elliptic.Descloux, Nassif, and Rappaz [4], [5] have studied the approximation of the

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Normal Modes of the Atlantic and Indian Oceans

Cited by 59 publications

References 0 publications

Observations of long period waves in the tropical oceans and atmosphere

Observations of long period waves in the tropical oceans and atmosphere

Multiple Oscillatory Modes of the Argentine Basin. Part II: The Spectral Origin of Basin Modes

Approximation of the Spectrum of Closed Operators: The Determination of Normal Modes of a Rotating Basin

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