Some Results in the Mathematical Theory of Seiches

Chrystal,

doi:10.1017/s0370164600008531

Cited by 19 publications

(7 citation statements)

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“…Tn = 2 l/n x/g h, where l= 28 km, h = 51 m yields T~ = 41.7 minutes, with a nodal line southeast of 'Meilen', the higher mode periods being an integral fraction of this. Early experiences [see Forel (1893), Schweitzer (1909), Chrystal (1904, 1905 and others] indicate that these results are likely to be inaccurate and thus necessitate application of bathymetry adjusted formulations. While Chrystal's channel formulation would suffice, since Coriolis effects have only insignificant influence, transverse structure of 3) Here, I is the lenght measured along the Thalweg, h the mean depth, g the gravity constant and n an integer.…”

Section: Lake Characteristicsmentioning

confidence: 99%

“…This formula was extended later by Du Boys (1891) to situations of basins with irregular shape. His formula is still approximate, and was soon replaced by the mathematically sounder theory of Chrystal (1904Chrystal ( , 1905 which permitted calculation of seiche periods in elongated basins with arbitrary shape. Of similar complexity is Defant's (1918) theory.…”

Section: Introductionmentioning

confidence: 99%

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The surface seiches of Lake of Zürich

Hutter

Raggio

Bucher

et al. 1982

Schweiz. Z. Hydrologie

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A computational analysis of the periods and structure of surface seiches of Lake of Ztirich and its experimental verification from three simultaneous water gauge recordings, mounted along the shores in Ziirich, Ps and Rapperswil is given. After a brief historical account the governing equations and the procedure, how they were discretized by a finite element technique are introduced. Computational results concern seiche periods and seiche structure, in particular co-range and co-tidal lines for the first seven free oscillations which are discussed in detail. Experimental verification is from recordings taken during January 1982. Inspection by eye allows identification of the three lowest order seiche periods including the phase shift between the recordings of Ztirich and Rapperswil. Higher order modes (up to order 19) are also detected by this method. Power spectral analysis including interstation phase shift and coherence allow identification of over fifteen seiche periods. Agreement between the theoretically predicted and experimentally determined periods is excellent for the first, second, third, fair for the fourth, fifth and sixth mode and good for the other higher modes, but statistical reliability is low for these.

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Section: Lake Characteristicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The surface seiches of Lake of Zürich

Hutter

Raggio

Bucher

et al. 1982

Schweiz. Z. Hydrologie

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“…The spatially one:dimensional Chrystal [ 1,2] equation valid for elongated basins, does not allow prediction of positively and negatively rotationg amphidromic systems, even when complemented by the Kelvin-wave dynamics approach but has the advantage of being computationally simple and in expensive. The curvature of the basin axis is ignored in this channel model and the selection of the axis is rather arbitrary so "there is an element of subjectivity in prescribing the channel axis which can cause error..." [5].…”

Section: Introductionmentioning

confidence: 99%

A chrystal-model describing gravitational barotropic motion in elongated lakes

Hutter

Raggio

1982

Arch. Met. Geoph. Biocl. A.

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SummaryA spatially one-dimensional model which extends the classical Chrystal equation and replaces the Kelvin wave dynamics approach is presented. It consists of a system of partial differential equations having the arc-length of a preselected lake axis and the time as independent variables and permits qualitatively and quantitatively correct prediction of gravitational waves in rotating systems. The general linear model accounting for bottom friction and atmospheric momentum input is specialized to a "first order" model and subsequently to a straight and ring shaped channel of constant depth. For the latter, a comparison of the dispersion relation of Kelvin-, Poincar~-and inertial-type waves with that of the two-dimensional tidal operator indicates that curvature effects of the lake can usually be ignored. Finally, results on co-range and co-tidal lines, obtained for lake of Lugano using extended models of different order prove that the simplest first order extension of the Chrystal equation is capable of predicting these with sufficient accuracy. Zusammenfassung

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“…The methods of Chrystal (1904Chrystal ( , 1905aChrystal ( , 1905b, Honda et a1. (1908), Proudman (1914), Defant (1918), Ertel (1933), and Hidaka (1936) are well known.…”

Section: Introductionmentioning

confidence: 99%

A new method for the computation of seiches in oblong basins

Germeles

1970

Tellus A: Dynamic Meteorology and Oceanography

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An iterative numerical method is presented for the computation of seiches in oblong lakes, bays and channels. The method is based on numerical forward integration of the governing equations and on an original iterative technique. Results from the application of the method to various basins show that the method is reliable, very stable and efficient. The application of the method to similar eigenvalue problems, occurring frequently in many branches of continuum mechanics, is discussed briefly. There is no apparent reason why the method would not be applicable to such problems.

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Some Results in the Mathematical Theory of Seiches

Cited by 19 publications

References 0 publications

The surface seiches of Lake of Zürich

The surface seiches of Lake of Zürich

A chrystal-model describing gravitational barotropic motion in elongated lakes

A new method for the computation of seiches in oblong basins

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