# The Shallow Water Wave Equations: Formulation, Analysis and Application Book

Part of the Lecture Notes in Engineering book series (LNENG, volume 15)

1. Front Matter
Pages I-XXV
2. Ingemar Kinnmark
Pages 1-11
3. Ingemar Kinnmark
Pages 12-26
4. Ingemar Kinnmark
Pages 27-37
5. Ingemar Kinnmark
Pages 38-67
6. Ingemar Kinnmark
Pages 68-95
7. Ingemar Kinnmark
Pages 96-114
8. Ingemar Kinnmark
Pages 115-147
9. Ingemar Kinnmark
Pages 148-158
10. Ingemar Kinnmark
Pages 159-171
11. Ingemar Kinnmark
Pages 172-175
12. Back Matter
Pages 176-187

### Introduction

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.

### Keywords

Fourier Analysis finite element method fluid friction information mass operator peat pressure pressure gradient stability water wave equation wind

#### Authors and affiliations

1. 1.Department of Civil EngineeringUniversity of Notre DameNotre DameUSA

### Bibliographic information

• Book Title The Shallow Water Wave Equations: Formulation, Analysis and Application
• Authors Ingemar Kinnmark
• Series Title Lecture Notes in Engineering
• DOI https://doi.org/10.1007/978-3-642-82646-7
• Copyright Information Springer-Verlag Berlin Heidelberg 1986
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Softcover ISBN 978-3-540-16031-1
• eBook ISBN 978-3-642-82646-7
• Series ISSN 0176-5035
• Edition Number 1
• Number of Pages XXVI, 188
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
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