Asymptotic Behaviour of Solutions to Laplace's Tidal Equations At Low Frequencies
The asymptotic behaviour of solutions to Laplace's tidal equations at low frequencies is considered. the method used is based on perturbation in small parameters, these being the ratios of tidal frequency and the coefficient of bottom friction to the angular frequency of the Earth's rotati...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Molodensky, Sergey M. [verfasserIn] |
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| Format: |
E-Artikel |
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| Erschienen: |
Oxford, UK: Blackwell Publishing Ltd ; 1989 |
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| Schlagwörter: |
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| Umfang: |
Online-Ressource |
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| Reproduktion: |
2007 ; Blackwell Publishing Journal Backfiles 1879-2005 |
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| Übergeordnetes Werk: |
In: Geophysical journal international - Oxford . Wiley-Blackwell, 1922, 97(1989), 3, Seite 0 |
| Übergeordnetes Werk: |
volume:97 ; year:1989 ; number:3 ; pages:0 |
| Links: |
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| DOI / URN: |
10.1111/j.1365-246X.1989.tb00516.x |
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NLEJ239638131 |
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| 520 | |a The asymptotic behaviour of solutions to Laplace's tidal equations at low frequencies is considered. the method used is based on perturbation in small parameters, these being the ratios of tidal frequency and the coefficient of bottom friction to the angular frequency of the Earth's rotation. It is shown that the resulting solutions are unstable in that the functions involved in the zero-order approximation are not uniquely determined by the zero-order equations, but depend on first-order terms as well. Because of this instability, direct methods of numerical integration are inefficient. We propose a different procedure, replacing the original set of equations in partial derivatives by ordinary differential equations that have a stable solution. the equations are examined qualitatively. It is shown, in particular, that for the case of an ocean of uniform depth over the whole Earth, they coincide with the well-known Lamb's equations. the asymptotic behaviour of the solutions is examined as modified by basin shape, bottom topography and bottom friction. | ||
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10.1111/j.1365-246X.1989.tb00516.x doi (DE-627)NLEJ239638131 DE-627 ger DE-627 rakwb Molodensky, Sergey M. verfasserin aut Asymptotic Behaviour of Solutions to Laplace's Tidal Equations At Low Frequencies Oxford, UK Blackwell Publishing Ltd 1989 Online-Ressource nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The asymptotic behaviour of solutions to Laplace's tidal equations at low frequencies is considered. the method used is based on perturbation in small parameters, these being the ratios of tidal frequency and the coefficient of bottom friction to the angular frequency of the Earth's rotation. It is shown that the resulting solutions are unstable in that the functions involved in the zero-order approximation are not uniquely determined by the zero-order equations, but depend on first-order terms as well. Because of this instability, direct methods of numerical integration are inefficient. We propose a different procedure, replacing the original set of equations in partial derivatives by ordinary differential equations that have a stable solution. the equations are examined qualitatively. It is shown, in particular, that for the case of an ocean of uniform depth over the whole Earth, they coincide with the well-known Lamb's equations. the asymptotic behaviour of the solutions is examined as modified by basin shape, bottom topography and bottom friction. 2007 Blackwell Publishing Journal Backfiles 1879-2005 |2007|||||||||| ocean model In Geophysical journal international Oxford . Wiley-Blackwell, 1922 97(1989), 3, Seite 0 Online-Ressource (DE-627)NLEJ243927827 (DE-600)2006420-2 1365-246X nnns volume:97 year:1989 number:3 pages:0 http://dx.doi.org/10.1111/j.1365-246X.1989.tb00516.x text/html Verlag Deutschlandweit zugänglich Volltext GBV_USEFLAG_U ZDB-1-DJB GBV_NL_ARTICLE AR 97 1989 3 0 |
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10.1111/j.1365-246X.1989.tb00516.x doi (DE-627)NLEJ239638131 DE-627 ger DE-627 rakwb Molodensky, Sergey M. verfasserin aut Asymptotic Behaviour of Solutions to Laplace's Tidal Equations At Low Frequencies Oxford, UK Blackwell Publishing Ltd 1989 Online-Ressource nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The asymptotic behaviour of solutions to Laplace's tidal equations at low frequencies is considered. the method used is based on perturbation in small parameters, these being the ratios of tidal frequency and the coefficient of bottom friction to the angular frequency of the Earth's rotation. It is shown that the resulting solutions are unstable in that the functions involved in the zero-order approximation are not uniquely determined by the zero-order equations, but depend on first-order terms as well. Because of this instability, direct methods of numerical integration are inefficient. We propose a different procedure, replacing the original set of equations in partial derivatives by ordinary differential equations that have a stable solution. the equations are examined qualitatively. It is shown, in particular, that for the case of an ocean of uniform depth over the whole Earth, they coincide with the well-known Lamb's equations. the asymptotic behaviour of the solutions is examined as modified by basin shape, bottom topography and bottom friction. 2007 Blackwell Publishing Journal Backfiles 1879-2005 |2007|||||||||| ocean model In Geophysical journal international Oxford . Wiley-Blackwell, 1922 97(1989), 3, Seite 0 Online-Ressource (DE-627)NLEJ243927827 (DE-600)2006420-2 1365-246X nnns volume:97 year:1989 number:3 pages:0 http://dx.doi.org/10.1111/j.1365-246X.1989.tb00516.x text/html Verlag Deutschlandweit zugänglich Volltext GBV_USEFLAG_U ZDB-1-DJB GBV_NL_ARTICLE AR 97 1989 3 0 |
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10.1111/j.1365-246X.1989.tb00516.x doi (DE-627)NLEJ239638131 DE-627 ger DE-627 rakwb Molodensky, Sergey M. verfasserin aut Asymptotic Behaviour of Solutions to Laplace's Tidal Equations At Low Frequencies Oxford, UK Blackwell Publishing Ltd 1989 Online-Ressource nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The asymptotic behaviour of solutions to Laplace's tidal equations at low frequencies is considered. the method used is based on perturbation in small parameters, these being the ratios of tidal frequency and the coefficient of bottom friction to the angular frequency of the Earth's rotation. It is shown that the resulting solutions are unstable in that the functions involved in the zero-order approximation are not uniquely determined by the zero-order equations, but depend on first-order terms as well. Because of this instability, direct methods of numerical integration are inefficient. We propose a different procedure, replacing the original set of equations in partial derivatives by ordinary differential equations that have a stable solution. the equations are examined qualitatively. It is shown, in particular, that for the case of an ocean of uniform depth over the whole Earth, they coincide with the well-known Lamb's equations. the asymptotic behaviour of the solutions is examined as modified by basin shape, bottom topography and bottom friction. 2007 Blackwell Publishing Journal Backfiles 1879-2005 |2007|||||||||| ocean model In Geophysical journal international Oxford . Wiley-Blackwell, 1922 97(1989), 3, Seite 0 Online-Ressource (DE-627)NLEJ243927827 (DE-600)2006420-2 1365-246X nnns volume:97 year:1989 number:3 pages:0 http://dx.doi.org/10.1111/j.1365-246X.1989.tb00516.x text/html Verlag Deutschlandweit zugänglich Volltext GBV_USEFLAG_U ZDB-1-DJB GBV_NL_ARTICLE AR 97 1989 3 0 |
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10.1111/j.1365-246X.1989.tb00516.x doi (DE-627)NLEJ239638131 DE-627 ger DE-627 rakwb Molodensky, Sergey M. verfasserin aut Asymptotic Behaviour of Solutions to Laplace's Tidal Equations At Low Frequencies Oxford, UK Blackwell Publishing Ltd 1989 Online-Ressource nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The asymptotic behaviour of solutions to Laplace's tidal equations at low frequencies is considered. the method used is based on perturbation in small parameters, these being the ratios of tidal frequency and the coefficient of bottom friction to the angular frequency of the Earth's rotation. It is shown that the resulting solutions are unstable in that the functions involved in the zero-order approximation are not uniquely determined by the zero-order equations, but depend on first-order terms as well. Because of this instability, direct methods of numerical integration are inefficient. We propose a different procedure, replacing the original set of equations in partial derivatives by ordinary differential equations that have a stable solution. the equations are examined qualitatively. It is shown, in particular, that for the case of an ocean of uniform depth over the whole Earth, they coincide with the well-known Lamb's equations. the asymptotic behaviour of the solutions is examined as modified by basin shape, bottom topography and bottom friction. 2007 Blackwell Publishing Journal Backfiles 1879-2005 |2007|||||||||| ocean model In Geophysical journal international Oxford . Wiley-Blackwell, 1922 97(1989), 3, Seite 0 Online-Ressource (DE-627)NLEJ243927827 (DE-600)2006420-2 1365-246X nnns volume:97 year:1989 number:3 pages:0 http://dx.doi.org/10.1111/j.1365-246X.1989.tb00516.x text/html Verlag Deutschlandweit zugänglich Volltext GBV_USEFLAG_U ZDB-1-DJB GBV_NL_ARTICLE AR 97 1989 3 0 |
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10.1111/j.1365-246X.1989.tb00516.x doi (DE-627)NLEJ239638131 DE-627 ger DE-627 rakwb Molodensky, Sergey M. verfasserin aut Asymptotic Behaviour of Solutions to Laplace's Tidal Equations At Low Frequencies Oxford, UK Blackwell Publishing Ltd 1989 Online-Ressource nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The asymptotic behaviour of solutions to Laplace's tidal equations at low frequencies is considered. the method used is based on perturbation in small parameters, these being the ratios of tidal frequency and the coefficient of bottom friction to the angular frequency of the Earth's rotation. It is shown that the resulting solutions are unstable in that the functions involved in the zero-order approximation are not uniquely determined by the zero-order equations, but depend on first-order terms as well. Because of this instability, direct methods of numerical integration are inefficient. We propose a different procedure, replacing the original set of equations in partial derivatives by ordinary differential equations that have a stable solution. the equations are examined qualitatively. It is shown, in particular, that for the case of an ocean of uniform depth over the whole Earth, they coincide with the well-known Lamb's equations. the asymptotic behaviour of the solutions is examined as modified by basin shape, bottom topography and bottom friction. 2007 Blackwell Publishing Journal Backfiles 1879-2005 |2007|||||||||| ocean model In Geophysical journal international Oxford . Wiley-Blackwell, 1922 97(1989), 3, Seite 0 Online-Ressource (DE-627)NLEJ243927827 (DE-600)2006420-2 1365-246X nnns volume:97 year:1989 number:3 pages:0 http://dx.doi.org/10.1111/j.1365-246X.1989.tb00516.x text/html Verlag Deutschlandweit zugänglich Volltext GBV_USEFLAG_U ZDB-1-DJB GBV_NL_ARTICLE AR 97 1989 3 0 |
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Asymptotic Behaviour of Solutions to Laplace's Tidal Equations At Low Frequencies |
| abstract |
The asymptotic behaviour of solutions to Laplace's tidal equations at low frequencies is considered. the method used is based on perturbation in small parameters, these being the ratios of tidal frequency and the coefficient of bottom friction to the angular frequency of the Earth's rotation. It is shown that the resulting solutions are unstable in that the functions involved in the zero-order approximation are not uniquely determined by the zero-order equations, but depend on first-order terms as well. Because of this instability, direct methods of numerical integration are inefficient. We propose a different procedure, replacing the original set of equations in partial derivatives by ordinary differential equations that have a stable solution. the equations are examined qualitatively. It is shown, in particular, that for the case of an ocean of uniform depth over the whole Earth, they coincide with the well-known Lamb's equations. the asymptotic behaviour of the solutions is examined as modified by basin shape, bottom topography and bottom friction. |
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The asymptotic behaviour of solutions to Laplace's tidal equations at low frequencies is considered. the method used is based on perturbation in small parameters, these being the ratios of tidal frequency and the coefficient of bottom friction to the angular frequency of the Earth's rotation. It is shown that the resulting solutions are unstable in that the functions involved in the zero-order approximation are not uniquely determined by the zero-order equations, but depend on first-order terms as well. Because of this instability, direct methods of numerical integration are inefficient. We propose a different procedure, replacing the original set of equations in partial derivatives by ordinary differential equations that have a stable solution. the equations are examined qualitatively. It is shown, in particular, that for the case of an ocean of uniform depth over the whole Earth, they coincide with the well-known Lamb's equations. the asymptotic behaviour of the solutions is examined as modified by basin shape, bottom topography and bottom friction. |
| abstract_unstemmed |
The asymptotic behaviour of solutions to Laplace's tidal equations at low frequencies is considered. the method used is based on perturbation in small parameters, these being the ratios of tidal frequency and the coefficient of bottom friction to the angular frequency of the Earth's rotation. It is shown that the resulting solutions are unstable in that the functions involved in the zero-order approximation are not uniquely determined by the zero-order equations, but depend on first-order terms as well. Because of this instability, direct methods of numerical integration are inefficient. We propose a different procedure, replacing the original set of equations in partial derivatives by ordinary differential equations that have a stable solution. the equations are examined qualitatively. It is shown, in particular, that for the case of an ocean of uniform depth over the whole Earth, they coincide with the well-known Lamb's equations. the asymptotic behaviour of the solutions is examined as modified by basin shape, bottom topography and bottom friction. |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">NLEJ239638131</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20210707092011.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">120426s1989 xx |||||o 00| ||und c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1111/j.1365-246X.1989.tb00516.x</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)NLEJ239638131</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Molodensky, Sergey M.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Asymptotic Behaviour of Solutions to Laplace's Tidal Equations At Low Frequencies</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Oxford, UK</subfield><subfield code="b">Blackwell Publishing Ltd</subfield><subfield code="c">1989</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zzz</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">z</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zu</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The asymptotic behaviour of solutions to Laplace's tidal equations at low frequencies is considered. the method used is based on perturbation in small parameters, these being the ratios of tidal frequency and the coefficient of bottom friction to the angular frequency of the Earth's rotation. It is shown that the resulting solutions are unstable in that the functions involved in the zero-order approximation are not uniquely determined by the zero-order equations, but depend on first-order terms as well. Because of this instability, direct methods of numerical integration are inefficient. We propose a different procedure, replacing the original set of equations in partial derivatives by ordinary differential equations that have a stable solution. the equations are examined qualitatively. It is shown, in particular, that for the case of an ocean of uniform depth over the whole Earth, they coincide with the well-known Lamb's equations. the asymptotic behaviour of the solutions is examined as modified by basin shape, bottom topography and bottom friction.</subfield></datafield><datafield tag="533" ind1=" " ind2=" "><subfield code="d">2007</subfield><subfield code="f">Blackwell Publishing Journal Backfiles 1879-2005</subfield><subfield code="7">|2007||||||||||</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">ocean model</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">In</subfield><subfield code="t">Geophysical journal international</subfield><subfield code="d">Oxford . Wiley-Blackwell, 1922</subfield><subfield code="g">97(1989), 3, Seite 0</subfield><subfield code="h">Online-Ressource</subfield><subfield code="w">(DE-627)NLEJ243927827</subfield><subfield code="w">(DE-600)2006420-2</subfield><subfield code="x">1365-246X</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:97</subfield><subfield code="g">year:1989</subfield><subfield code="g">number:3</subfield><subfield code="g">pages:0</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://dx.doi.org/10.1111/j.1365-246X.1989.tb00516.x</subfield><subfield code="q">text/html</subfield><subfield code="x">Verlag</subfield><subfield code="z">Deutschlandweit zugänglich</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-1-DJB</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_NL_ARTICLE</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">97</subfield><subfield code="j">1989</subfield><subfield code="e">3</subfield><subfield code="h">0</subfield></datafield></record></collection>
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