Title: Nonlinear Long Wave in Shallow Water
1Nonlinear Long Wave in Shallow Water
2Contents
- Two Important Parameters For Waves In Shallow
Water - Nondimensional Variables
- Nondimensional Governing Equation Boundary
Conditions - Perturbation Series of Potential
- Depth Average Horizontal Velocity Wave
Elevation - Ariy's Approximation
- Boussenesq's Approximation
- Steady Kdv Equation
- Solitary Wave
- Cnoidal Wave
3Two Important Nonlinear Parameters for Waves in
Shallow Water
4Non-dimensional Variables
5Nondimensional Governing Equation Boundary
Conditions
6Perturbation Series for Potential
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8 Depth Average Horizontal Velocity Wave
Elevation
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11Ariy's Theory For Very Long Very Steep Waves
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13Boussinesq's Approximation
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15Steady KdV (Korteweg-de Vries) Equation
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19Solitary Waves
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21Figure 1. The sketch of a non-dimensional
solitary wave train.
22Cnoidal Wave
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32- Computation Procedure
- When water depth h, wave length L (or T) and wave
- height H are given, we may use a try and error
(or iterative) method to determine m based on
Equation (50) (or (53)). - Once m is obtained, the characteristics of a
Cnoidal - wave train can be computed using Equations (47),
(48), (49), (51) (52).