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The Shallow Water Wave Equations: Formulation, Analysis and Application

  • Ingemar Kinnmark
Book

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

Table of contents

  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 96-114
  7. Ingemar Kinnmark
    Pages 115-147
  8. Ingemar Kinnmark
    Pages 148-158
  9. Ingemar Kinnmark
    Pages 159-171
  10. Ingemar Kinnmark
    Pages 172-175
  11. Back Matter
    Pages 176-187

About this book

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

  • Ingemar Kinnmark
    • 1
  1. 1.Department of Civil EngineeringUniversity of Notre DameNotre DameUSA

Bibliographic information

  • 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 Springer Book Archive
  • Print ISBN 978-3-540-16031-1
  • Online ISBN 978-3-642-82646-7
  • Series Print ISSN 0176-5035
  • Buy this book on publisher's site
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