Lecture Notes in Engineering

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

Authors: Kinnmark, Ingemar

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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.

• Introduction

Pages 1-11

Kinnmark, Ingemar

• Equation Formulation

Pages 12-26

Kinnmark, Ingemar

• Fourier Analysis Methods

Pages 27-37

Kinnmark, Ingemar

• Stability

Pages 38-67

Kinnmark, Ingemar

• Explicit Methods using Various Spatial Discretizations

Pages 68-95

Kinnmark, Ingemar

eBook $109.00 price for USA in USD • ISBN 978-3-642-82646-7 • Digitally watermarked, DRM-free • Included format: • ebooks can be used on all reading devices • Immediate eBook download after purchase Softcover$149.99
price for USA in USD
• ISBN 978-3-540-16031-1
• Free shipping for individuals worldwide
• Institutional customers should get in touch with their account manager
• Covid-19 shipping restrictions
• Usually ready to be dispatched within 3 to 5 business days, if in stock

## Bibliographic Information

Bibliographic Information
Book Title
The Shallow Water Wave Equations: Formulation, Analysis and Application
Authors
Series Title
Lecture Notes in Engineering
Series Volume
15
1986
Publisher
Springer-Verlag Berlin Heidelberg
Springer-Verlag Berlin, Heidelberg
eBook ISBN
978-3-642-82646-7
DOI
10.1007/978-3-642-82646-7
Softcover ISBN
978-3-540-16031-1
Series ISSN
0176-5035
Edition Number
1
Number of Pages
XXVI, 188
Topics