The Shallow Water Wave Equations: Formulation, Analysis and Application:
1. 1 AREAS OF APPLICATION FOR THE SHALLOW WATER EQUATIONS The shallow water equations describe conservation of mass and mo mentum in a fluid. They may be expressed in the primitive equation form Continuity Equation _ a, + V. (Hv) = 0 L(l;,v;h) at (1. 1) Non-Conservative Momentum Equations a M("...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1986
|
| Schriftenreihe: | Lecture Notes in Engineering
15 |
| Schlagworte: | |
| Online-Zugang: | BTU01 URL des Erstveröffentlichers |
| Zusammenfassung: | 1. 1 AREAS OF APPLICATION FOR THE SHALLOW WATER EQUATIONS The shallow water equations describe conservation of mass and mo mentum in a fluid. They may be expressed in the primitive equation form Continuity Equation _ a, + V. (Hv) = 0 L(l;,v;h) at (1. 1) Non-Conservative Momentum Equations a M("vjt,f,g,h,A) = at(v) + (v. V)v + tv - fkxv + gV, - AIH = 0 (1. 2) 2 where is elevation above a datum (L) ~ h is bathymetry (L) H = h + C is total fluid depth (L) v is vertically averaged fluid velocity in eastward direction (x) and northward direction (y) (LIT) t is the non-linear friction coefficient (liT) f is the Coriolis parameter (liT) is acceleration due to gravity (L/T2) g A is atmospheric (wind) forcing in eastward direction (x) and northward direction (y) (L2/T2) v is the gradient operator (IlL) k is a unit vector in the vertical direction (1) x is positive eastward (L) is positive northward (L) Y t is time (T) These Non-Conservative Momentum Equations may be compared to the Conservative Momentum Equations (2. 4). The latter originate directly from a vertical integration of a momentum balance over a fluid ele ment. The former are obtained indirectly, through subtraction of the continuity equation from the latter. Equations (1. 1) and (1. 2) are valid under the following assumptions: 1. The fluid is well-mixed vertically with a hydrostatic pressure gradient. 2. The density of the fluid is constant |
| Beschreibung: | 1 Online-Ressource (XXVI, 188 p) |
| ISBN: | 9783642826467 |
| DOI: | 10.1007/978-3-642-82646-7 |
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| 520 | |a 1. 1 AREAS OF APPLICATION FOR THE SHALLOW WATER EQUATIONS The shallow water equations describe conservation of mass and mo mentum in a fluid. They may be expressed in the primitive equation form Continuity Equation _ a, + V. (Hv) = 0 L(l;,v;h) at (1. 1) Non-Conservative Momentum Equations a M("vjt,f,g,h,A) = at(v) + (v. V)v + tv - fkxv + gV, - AIH = 0 (1. 2) 2 where is elevation above a datum (L) ~ h is bathymetry (L) H = h + C is total fluid depth (L) v is vertically averaged fluid velocity in eastward direction (x) and northward direction (y) (LIT) t is the non-linear friction coefficient (liT) f is the Coriolis parameter (liT) is acceleration due to gravity (L/T2) g A is atmospheric (wind) forcing in eastward direction (x) and northward direction (y) (L2/T2) v is the gradient operator (IlL) k is a unit vector in the vertical direction (1) x is positive eastward (L) is positive northward (L) Y t is time (T) These Non-Conservative Momentum Equations may be compared to the Conservative Momentum Equations (2. 4). The latter originate directly from a vertical integration of a momentum balance over a fluid ele ment. The former are obtained indirectly, through subtraction of the continuity equation from the latter. Equations (1. 1) and (1. 2) are valid under the following assumptions: 1. The fluid is well-mixed vertically with a hydrostatic pressure gradient. 2. The density of the fluid is constant | ||
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| id | DE-604.BV045186818 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:10:58Z |
| institution | BVB |
| isbn | 9783642826467 |
| language | English |
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| record_format | marc |
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| spelling | Kinnmark, Ingemar Verfasser aut The Shallow Water Wave Equations: Formulation, Analysis and Application by Ingemar Kinnmark Berlin, Heidelberg Springer Berlin Heidelberg 1986 1 Online-Ressource (XXVI, 188 p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Engineering 15 1. 1 AREAS OF APPLICATION FOR THE SHALLOW WATER EQUATIONS The shallow water equations describe conservation of mass and mo mentum in a fluid. They may be expressed in the primitive equation form Continuity Equation _ a, + V. (Hv) = 0 L(l;,v;h) at (1. 1) Non-Conservative Momentum Equations a M("vjt,f,g,h,A) = at(v) + (v. V)v + tv - fkxv + gV, - AIH = 0 (1. 2) 2 where is elevation above a datum (L) ~ h is bathymetry (L) H = h + C is total fluid depth (L) v is vertically averaged fluid velocity in eastward direction (x) and northward direction (y) (LIT) t is the non-linear friction coefficient (liT) f is the Coriolis parameter (liT) is acceleration due to gravity (L/T2) g A is atmospheric (wind) forcing in eastward direction (x) and northward direction (y) (L2/T2) v is the gradient operator (IlL) k is a unit vector in the vertical direction (1) x is positive eastward (L) is positive northward (L) Y t is time (T) These Non-Conservative Momentum Equations may be compared to the Conservative Momentum Equations (2. 4). The latter originate directly from a vertical integration of a momentum balance over a fluid ele ment. The former are obtained indirectly, through subtraction of the continuity equation from the latter. Equations (1. 1) and (1. 2) are valid under the following assumptions: 1. The fluid is well-mixed vertically with a hydrostatic pressure gradient. 2. The density of the fluid is constant Engineering Geoengineering, Foundations, Hydraulics Waste Water Technology / Water Pollution Control / Water Management / Aquatic Pollution Engineering geology Engineering / Geology Foundations Hydraulics Water pollution Flachwasser (DE-588)4121276-9 gnd rswk-swf Wasserwelle (DE-588)4136091-6 gnd rswk-swf Wasserwelle (DE-588)4136091-6 s Flachwasser (DE-588)4121276-9 s 1\p DE-604 Erscheint auch als Druck-Ausgabe 9783540160311 https://doi.org/10.1007/978-3-642-82646-7 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kinnmark, Ingemar The Shallow Water Wave Equations: Formulation, Analysis and Application Engineering Geoengineering, Foundations, Hydraulics Waste Water Technology / Water Pollution Control / Water Management / Aquatic Pollution Engineering geology Engineering / Geology Foundations Hydraulics Water pollution Flachwasser (DE-588)4121276-9 gnd Wasserwelle (DE-588)4136091-6 gnd |
| subject_GND | (DE-588)4121276-9 (DE-588)4136091-6 |
| title | The Shallow Water Wave Equations: Formulation, Analysis and Application |
| title_auth | The Shallow Water Wave Equations: Formulation, Analysis and Application |
| title_exact_search | The Shallow Water Wave Equations: Formulation, Analysis and Application |
| title_full | The Shallow Water Wave Equations: Formulation, Analysis and Application by Ingemar Kinnmark |
| title_fullStr | The Shallow Water Wave Equations: Formulation, Analysis and Application by Ingemar Kinnmark |
| title_full_unstemmed | The Shallow Water Wave Equations: Formulation, Analysis and Application by Ingemar Kinnmark |
| title_short | The Shallow Water Wave Equations: Formulation, Analysis and Application |
| title_sort | the shallow water wave equations formulation analysis and application |
| topic | Engineering Geoengineering, Foundations, Hydraulics Waste Water Technology / Water Pollution Control / Water Management / Aquatic Pollution Engineering geology Engineering / Geology Foundations Hydraulics Water pollution Flachwasser (DE-588)4121276-9 gnd Wasserwelle (DE-588)4136091-6 gnd |
| topic_facet | Engineering Geoengineering, Foundations, Hydraulics Waste Water Technology / Water Pollution Control / Water Management / Aquatic Pollution Engineering geology Engineering / Geology Foundations Hydraulics Water pollution Flachwasser Wasserwelle |
| url | https://doi.org/10.1007/978-3-642-82646-7 |
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