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Coastal Engineering: Theory and Practice
breaking, surface tension, nonlinear interaction are generally represented as
Boussinesq-type équations. However, in engineering applications, the équations are often extended beyond the breaking point, up to wave run-up in
the swash zone. This is possible by adding an artificial energy dissipation
term for wave breaking. Besides, efforts are also made to extend the model
to deeper water. Unlike the wave spectral model and the MSE model, the
Boussinesq model does not hâve the presumption that the flow is periodic.
Therefore, it can be applied to waves induced by impulsive motions, i.e.,
solitary waves, landslide-induced waves, tsunami, and unsteady undulation
in open channels (Lin, 2008).
Some of the simplified form of Boussinesq équations based on the
assumption of waves travel along one direction hâve spécifie applications
as listed below.
a. Equation of wave propagation in one dimension is called Korteweg-de
Vries équation: both non-periodic solitary waves and periodic cnoidal
waves can be derived from fcdV équation, i.e., approximated solutions of
the Boussinesq équations.
b. Equation of wave propagation in two dimension is called KadomtsevPetviashvili équation
c. The nonlinear Schrôdinger équation (NLS équation) is for the complex
valued amplitude of narrowband waves.
10.7.2 Shallow-water équation wave models
To model tsunami or other long waves (e.g., tides), a shallow-water équation
(SWE) model is more likely to be adopted. Compared with the Boussinesq
model, the SWE model is simpler because the flow is assumed to be uniform
across the water depth and the wave-dispersive effect is neglected. The SWE
model has a wide application range in modelling tsunami, tides, storm
surges, and river flows. The main limitation of the SWE model is that it is
suitable only for flows whose horizontal scale is much larger than vertical
scale (Lin, 2008).
References
Anand K. V., Sannasiraj, S. A. and Sundar, V. (2014). Investigation on the
cyclonic sea State along Southeast Coast of India, Marine Geodesy, 38, 58-78.
Berkhoff, J. C. W. (1972). Computation of combined refraction-diffraction, Proc.
13th Int. Conf. Coastal Engineering, pp. 471-90.
Booij, N. (1983). A note on the accuracy of the mild slope équation, Coastal Eng.,
7, 191-203.
Coastal Engineering: Theory and Practice
breaking, surface tension, nonlinear interaction are generally represented as
Boussinesq-type équations. However, in engineering applications, the équations are often extended beyond the breaking point, up to wave run-up in
the swash zone. This is possible by adding an artificial energy dissipation
term for wave breaking. Besides, efforts are also made to extend the model
to deeper water. Unlike the wave spectral model and the MSE model, the
Boussinesq model does not hâve the presumption that the flow is periodic.
Therefore, it can be applied to waves induced by impulsive motions, i.e.,
solitary waves, landslide-induced waves, tsunami, and unsteady undulation
in open channels (Lin, 2008).
Some of the simplified form of Boussinesq équations based on the
assumption of waves travel along one direction hâve spécifie applications
as listed below.
a. Equation of wave propagation in one dimension is called Korteweg-de
Vries équation: both non-periodic solitary waves and periodic cnoidal
waves can be derived from fcdV équation, i.e., approximated solutions of
the Boussinesq équations.
b. Equation of wave propagation in two dimension is called KadomtsevPetviashvili équation
c. The nonlinear Schrôdinger équation (NLS équation) is for the complex
valued amplitude of narrowband waves.
10.7.2 Shallow-water équation wave models
To model tsunami or other long waves (e.g., tides), a shallow-water équation
(SWE) model is more likely to be adopted. Compared with the Boussinesq
model, the SWE model is simpler because the flow is assumed to be uniform
across the water depth and the wave-dispersive effect is neglected. The SWE
model has a wide application range in modelling tsunami, tides, storm
surges, and river flows. The main limitation of the SWE model is that it is
suitable only for flows whose horizontal scale is much larger than vertical
scale (Lin, 2008).
References
Anand K. V., Sannasiraj, S. A. and Sundar, V. (2014). Investigation on the
cyclonic sea State along Southeast Coast of India, Marine Geodesy, 38, 58-78.
Berkhoff, J. C. W. (1972). Computation of combined refraction-diffraction, Proc.
13th Int. Conf. Coastal Engineering, pp. 471-90.
Booij, N. (1983). A note on the accuracy of the mild slope équation, Coastal Eng.,
7, 191-203.