Conservation of mechanical energy and circulation in the theory of inviscid fluid sheets
Abstract In the theory of thin fluid sheets, governing equations are derived with specific reference to an assumed simple kinematic structure of the flow. There is a separate set of governing equations associated with each degree of complexity of the kinematic structure, forming a hierarchy of model...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Shields, J. J. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1989 |
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| Schlagwörter: |
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| Anmerkung: |
© Kluwer Academic Publishers 1989 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of engineering mathematics - Kluwer Academic Publishers, 1967, 23(1989), 1 vom: März, Seite 1-15 |
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| Übergeordnetes Werk: |
volume:23 ; year:1989 ; number:1 ; month:03 ; pages:1-15 |
| Links: |
|---|
| DOI / URN: |
10.1007/BF00058430 |
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| Katalog-ID: |
OLC2074030681 |
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| 520 | |a Abstract In the theory of thin fluid sheets, governing equations are derived with specific reference to an assumed simple kinematic structure of the flow. There is a separate set of governing equations associated with each degree of complexity of the kinematic structure, forming a hierarchy of models (Green and Naghdi [3] and Shields and Webster [8]). If one is interested in the velocity profile across the sheet, the kinematic structure can be used again to interpret the variables in the governing equations as an approximate flow. This paper is concerned with the properties of this approximate flow. Two important consequences of the field equations (Euler's equations) in the classical, three-dimensional theory of ideal fluids are: conservation of mechanical energy, and conservation of circulation (Kelvin's theorem). The research reported herein provides a proof that mechanical energy is exactly conserved for the approximate flow in each level in this hierarchy. Two types of circulation are considered in the approximate flow: “in-sheet” circulation which is computed about circuits lying a fixed fractional distance between the top and bottom surfaces of the sheet, and “cross-sheet” circulation which is computed about circuits lying in a vertical cylindrical surface. It was found that K moments of the in-sheet circulation and K − 1 weighted moments of the cross-sheet circulation are conserved in the Kth level approximate flow. | ||
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10.1007/BF00058430 doi (DE-627)OLC2074030681 (DE-He213)BF00058430-p DE-627 ger DE-627 rakwb eng 510 VZ Shields, J. J. verfasserin aut Conservation of mechanical energy and circulation in the theory of inviscid fluid sheets 1989 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic Publishers 1989 Abstract In the theory of thin fluid sheets, governing equations are derived with specific reference to an assumed simple kinematic structure of the flow. There is a separate set of governing equations associated with each degree of complexity of the kinematic structure, forming a hierarchy of models (Green and Naghdi [3] and Shields and Webster [8]). If one is interested in the velocity profile across the sheet, the kinematic structure can be used again to interpret the variables in the governing equations as an approximate flow. This paper is concerned with the properties of this approximate flow. Two important consequences of the field equations (Euler's equations) in the classical, three-dimensional theory of ideal fluids are: conservation of mechanical energy, and conservation of circulation (Kelvin's theorem). The research reported herein provides a proof that mechanical energy is exactly conserved for the approximate flow in each level in this hierarchy. Two types of circulation are considered in the approximate flow: “in-sheet” circulation which is computed about circuits lying a fixed fractional distance between the top and bottom surfaces of the sheet, and “cross-sheet” circulation which is computed about circuits lying in a vertical cylindrical surface. It was found that K moments of the in-sheet circulation and K − 1 weighted moments of the cross-sheet circulation are conserved in the Kth level approximate flow. Velocity Profile Governing Equation Industrial Mathematic Specific Reference Field Equation Webster, W. C. aut Enthalten in Journal of engineering mathematics Kluwer Academic Publishers, 1967 23(1989), 1 vom: März, Seite 1-15 (DE-627)129595748 (DE-600)240689-5 (DE-576)015088766 0022-0833 nnns volume:23 year:1989 number:1 month:03 pages:1-15 https://doi.org/10.1007/BF00058430 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_32 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2088 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4307 GBV_ILN_4309 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4700 AR 23 1989 1 03 1-15 |
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10.1007/BF00058430 doi (DE-627)OLC2074030681 (DE-He213)BF00058430-p DE-627 ger DE-627 rakwb eng 510 VZ Shields, J. J. verfasserin aut Conservation of mechanical energy and circulation in the theory of inviscid fluid sheets 1989 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic Publishers 1989 Abstract In the theory of thin fluid sheets, governing equations are derived with specific reference to an assumed simple kinematic structure of the flow. There is a separate set of governing equations associated with each degree of complexity of the kinematic structure, forming a hierarchy of models (Green and Naghdi [3] and Shields and Webster [8]). If one is interested in the velocity profile across the sheet, the kinematic structure can be used again to interpret the variables in the governing equations as an approximate flow. This paper is concerned with the properties of this approximate flow. Two important consequences of the field equations (Euler's equations) in the classical, three-dimensional theory of ideal fluids are: conservation of mechanical energy, and conservation of circulation (Kelvin's theorem). The research reported herein provides a proof that mechanical energy is exactly conserved for the approximate flow in each level in this hierarchy. Two types of circulation are considered in the approximate flow: “in-sheet” circulation which is computed about circuits lying a fixed fractional distance between the top and bottom surfaces of the sheet, and “cross-sheet” circulation which is computed about circuits lying in a vertical cylindrical surface. It was found that K moments of the in-sheet circulation and K − 1 weighted moments of the cross-sheet circulation are conserved in the Kth level approximate flow. Velocity Profile Governing Equation Industrial Mathematic Specific Reference Field Equation Webster, W. C. aut Enthalten in Journal of engineering mathematics Kluwer Academic Publishers, 1967 23(1989), 1 vom: März, Seite 1-15 (DE-627)129595748 (DE-600)240689-5 (DE-576)015088766 0022-0833 nnns volume:23 year:1989 number:1 month:03 pages:1-15 https://doi.org/10.1007/BF00058430 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_32 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2088 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4307 GBV_ILN_4309 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4700 AR 23 1989 1 03 1-15 |
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10.1007/BF00058430 doi (DE-627)OLC2074030681 (DE-He213)BF00058430-p DE-627 ger DE-627 rakwb eng 510 VZ Shields, J. J. verfasserin aut Conservation of mechanical energy and circulation in the theory of inviscid fluid sheets 1989 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic Publishers 1989 Abstract In the theory of thin fluid sheets, governing equations are derived with specific reference to an assumed simple kinematic structure of the flow. There is a separate set of governing equations associated with each degree of complexity of the kinematic structure, forming a hierarchy of models (Green and Naghdi [3] and Shields and Webster [8]). If one is interested in the velocity profile across the sheet, the kinematic structure can be used again to interpret the variables in the governing equations as an approximate flow. This paper is concerned with the properties of this approximate flow. Two important consequences of the field equations (Euler's equations) in the classical, three-dimensional theory of ideal fluids are: conservation of mechanical energy, and conservation of circulation (Kelvin's theorem). The research reported herein provides a proof that mechanical energy is exactly conserved for the approximate flow in each level in this hierarchy. Two types of circulation are considered in the approximate flow: “in-sheet” circulation which is computed about circuits lying a fixed fractional distance between the top and bottom surfaces of the sheet, and “cross-sheet” circulation which is computed about circuits lying in a vertical cylindrical surface. It was found that K moments of the in-sheet circulation and K − 1 weighted moments of the cross-sheet circulation are conserved in the Kth level approximate flow. Velocity Profile Governing Equation Industrial Mathematic Specific Reference Field Equation Webster, W. C. aut Enthalten in Journal of engineering mathematics Kluwer Academic Publishers, 1967 23(1989), 1 vom: März, Seite 1-15 (DE-627)129595748 (DE-600)240689-5 (DE-576)015088766 0022-0833 nnns volume:23 year:1989 number:1 month:03 pages:1-15 https://doi.org/10.1007/BF00058430 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_32 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2088 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4307 GBV_ILN_4309 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4700 AR 23 1989 1 03 1-15 |
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10.1007/BF00058430 doi (DE-627)OLC2074030681 (DE-He213)BF00058430-p DE-627 ger DE-627 rakwb eng 510 VZ Shields, J. J. verfasserin aut Conservation of mechanical energy and circulation in the theory of inviscid fluid sheets 1989 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic Publishers 1989 Abstract In the theory of thin fluid sheets, governing equations are derived with specific reference to an assumed simple kinematic structure of the flow. There is a separate set of governing equations associated with each degree of complexity of the kinematic structure, forming a hierarchy of models (Green and Naghdi [3] and Shields and Webster [8]). If one is interested in the velocity profile across the sheet, the kinematic structure can be used again to interpret the variables in the governing equations as an approximate flow. This paper is concerned with the properties of this approximate flow. Two important consequences of the field equations (Euler's equations) in the classical, three-dimensional theory of ideal fluids are: conservation of mechanical energy, and conservation of circulation (Kelvin's theorem). The research reported herein provides a proof that mechanical energy is exactly conserved for the approximate flow in each level in this hierarchy. Two types of circulation are considered in the approximate flow: “in-sheet” circulation which is computed about circuits lying a fixed fractional distance between the top and bottom surfaces of the sheet, and “cross-sheet” circulation which is computed about circuits lying in a vertical cylindrical surface. It was found that K moments of the in-sheet circulation and K − 1 weighted moments of the cross-sheet circulation are conserved in the Kth level approximate flow. Velocity Profile Governing Equation Industrial Mathematic Specific Reference Field Equation Webster, W. C. aut Enthalten in Journal of engineering mathematics Kluwer Academic Publishers, 1967 23(1989), 1 vom: März, Seite 1-15 (DE-627)129595748 (DE-600)240689-5 (DE-576)015088766 0022-0833 nnns volume:23 year:1989 number:1 month:03 pages:1-15 https://doi.org/10.1007/BF00058430 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_32 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2088 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4307 GBV_ILN_4309 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4700 AR 23 1989 1 03 1-15 |
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10.1007/BF00058430 doi (DE-627)OLC2074030681 (DE-He213)BF00058430-p DE-627 ger DE-627 rakwb eng 510 VZ Shields, J. J. verfasserin aut Conservation of mechanical energy and circulation in the theory of inviscid fluid sheets 1989 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic Publishers 1989 Abstract In the theory of thin fluid sheets, governing equations are derived with specific reference to an assumed simple kinematic structure of the flow. There is a separate set of governing equations associated with each degree of complexity of the kinematic structure, forming a hierarchy of models (Green and Naghdi [3] and Shields and Webster [8]). If one is interested in the velocity profile across the sheet, the kinematic structure can be used again to interpret the variables in the governing equations as an approximate flow. This paper is concerned with the properties of this approximate flow. Two important consequences of the field equations (Euler's equations) in the classical, three-dimensional theory of ideal fluids are: conservation of mechanical energy, and conservation of circulation (Kelvin's theorem). The research reported herein provides a proof that mechanical energy is exactly conserved for the approximate flow in each level in this hierarchy. Two types of circulation are considered in the approximate flow: “in-sheet” circulation which is computed about circuits lying a fixed fractional distance between the top and bottom surfaces of the sheet, and “cross-sheet” circulation which is computed about circuits lying in a vertical cylindrical surface. It was found that K moments of the in-sheet circulation and K − 1 weighted moments of the cross-sheet circulation are conserved in the Kth level approximate flow. Velocity Profile Governing Equation Industrial Mathematic Specific Reference Field Equation Webster, W. C. aut Enthalten in Journal of engineering mathematics Kluwer Academic Publishers, 1967 23(1989), 1 vom: März, Seite 1-15 (DE-627)129595748 (DE-600)240689-5 (DE-576)015088766 0022-0833 nnns volume:23 year:1989 number:1 month:03 pages:1-15 https://doi.org/10.1007/BF00058430 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_32 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2088 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4307 GBV_ILN_4309 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4700 AR 23 1989 1 03 1-15 |
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Journal of engineering mathematics |
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Conservation of mechanical energy and circulation in the theory of inviscid fluid sheets |
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Conservation of mechanical energy and circulation in the theory of inviscid fluid sheets |
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Shields, J. J. |
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Journal of engineering mathematics |
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1989 |
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Shields, J. J. Webster, W. C. |
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Shields, J. J. |
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10.1007/BF00058430 |
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510 |
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conservation of mechanical energy and circulation in the theory of inviscid fluid sheets |
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Conservation of mechanical energy and circulation in the theory of inviscid fluid sheets |
| abstract |
Abstract In the theory of thin fluid sheets, governing equations are derived with specific reference to an assumed simple kinematic structure of the flow. There is a separate set of governing equations associated with each degree of complexity of the kinematic structure, forming a hierarchy of models (Green and Naghdi [3] and Shields and Webster [8]). If one is interested in the velocity profile across the sheet, the kinematic structure can be used again to interpret the variables in the governing equations as an approximate flow. This paper is concerned with the properties of this approximate flow. Two important consequences of the field equations (Euler's equations) in the classical, three-dimensional theory of ideal fluids are: conservation of mechanical energy, and conservation of circulation (Kelvin's theorem). The research reported herein provides a proof that mechanical energy is exactly conserved for the approximate flow in each level in this hierarchy. Two types of circulation are considered in the approximate flow: “in-sheet” circulation which is computed about circuits lying a fixed fractional distance between the top and bottom surfaces of the sheet, and “cross-sheet” circulation which is computed about circuits lying in a vertical cylindrical surface. It was found that K moments of the in-sheet circulation and K − 1 weighted moments of the cross-sheet circulation are conserved in the Kth level approximate flow. © Kluwer Academic Publishers 1989 |
| abstractGer |
Abstract In the theory of thin fluid sheets, governing equations are derived with specific reference to an assumed simple kinematic structure of the flow. There is a separate set of governing equations associated with each degree of complexity of the kinematic structure, forming a hierarchy of models (Green and Naghdi [3] and Shields and Webster [8]). If one is interested in the velocity profile across the sheet, the kinematic structure can be used again to interpret the variables in the governing equations as an approximate flow. This paper is concerned with the properties of this approximate flow. Two important consequences of the field equations (Euler's equations) in the classical, three-dimensional theory of ideal fluids are: conservation of mechanical energy, and conservation of circulation (Kelvin's theorem). The research reported herein provides a proof that mechanical energy is exactly conserved for the approximate flow in each level in this hierarchy. Two types of circulation are considered in the approximate flow: “in-sheet” circulation which is computed about circuits lying a fixed fractional distance between the top and bottom surfaces of the sheet, and “cross-sheet” circulation which is computed about circuits lying in a vertical cylindrical surface. It was found that K moments of the in-sheet circulation and K − 1 weighted moments of the cross-sheet circulation are conserved in the Kth level approximate flow. © Kluwer Academic Publishers 1989 |
| abstract_unstemmed |
Abstract In the theory of thin fluid sheets, governing equations are derived with specific reference to an assumed simple kinematic structure of the flow. There is a separate set of governing equations associated with each degree of complexity of the kinematic structure, forming a hierarchy of models (Green and Naghdi [3] and Shields and Webster [8]). If one is interested in the velocity profile across the sheet, the kinematic structure can be used again to interpret the variables in the governing equations as an approximate flow. This paper is concerned with the properties of this approximate flow. Two important consequences of the field equations (Euler's equations) in the classical, three-dimensional theory of ideal fluids are: conservation of mechanical energy, and conservation of circulation (Kelvin's theorem). The research reported herein provides a proof that mechanical energy is exactly conserved for the approximate flow in each level in this hierarchy. Two types of circulation are considered in the approximate flow: “in-sheet” circulation which is computed about circuits lying a fixed fractional distance between the top and bottom surfaces of the sheet, and “cross-sheet” circulation which is computed about circuits lying in a vertical cylindrical surface. It was found that K moments of the in-sheet circulation and K − 1 weighted moments of the cross-sheet circulation are conserved in the Kth level approximate flow. © Kluwer Academic Publishers 1989 |
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Conservation of mechanical energy and circulation in the theory of inviscid fluid sheets |
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