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Stability of steady gravity waves generated by a moving localised pressure disturbance in water of finite depth
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10.1063/1.4812285
/content/aip/journal/pof2/25/7/10.1063/1.4812285
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/7/10.1063/1.4812285
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Steady state downstream wavetrain for subcritical flow = 0.63, with Gaussian forcing (9) and ε = 0.1, = 2.

Image of FIG. 2.
FIG. 2.

Steady state wave-free solution for subcritical flow = 0.5, and the same forcing as in Figure 1 .

Image of FIG. 3.
FIG. 3.

Steady branches of subcritical flow, showing the relationship between and the amplitude of the downstream wavetrain, with Gaussian forcing (9) and = 2.

Image of FIG. 4.
FIG. 4.

Supercritical steady waves with = 1.55, for the same forcing as in Figure 1 .

Image of FIG. 5.
FIG. 5.

Steady branches of supercritical flow, showing the relationship between and the amplitude α of the localised steady solitary-like wave, for the Gaussian forcing (9) and = 2.

Image of FIG. 6.
FIG. 6.

Evolution of the free surface profiles from the fKdV model (left) and the fully nonlinear simulations (right) for Froude number = 0.8, 0.9, 1.0, 1.1, 1.2 (top to bottom), with Gaussian forcing (9) and ε = 0.01, = 2.

Image of FIG. 7.
FIG. 7.

As for Figure 6 but with ε = 0.1.

Image of FIG. 8.
FIG. 8.

Nonlinear evolution of subcritical free surface profile for = 0.8, with Gaussian forcing (9) and ε = 0.001, = 2.

Image of FIG. 9.
FIG. 9.

Comparison of steady and unsteady solutions, for subcritical free surface profiles, with = 0.8 and the same forcing as in Figure 8 .

Image of FIG. 10.
FIG. 10.

Nonlinear evolution of supercritical free surface profile for = 1.2, with Gaussian forcing (9) and ε = 0.001, = 2. The initial condition is the lower branch steady solution, see Figure 5 .

Image of FIG. 11.
FIG. 11.

Nonlinear evolution of supercritical free surface profile for = 1.2, with Gaussian forcing (9) and ε = 0.001, = 2, and the initial condition from the upper branch.

Image of FIG. 12.
FIG. 12.

As for Figure 11 but using the fKdV model.

Image of FIG. 13.
FIG. 13.

Nonlinear evolution of a supercritical free surface profile for = 1.1, with Gaussian forcing (9) and ε = 0.001, = 2, and initial condition from the upper branch.

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/content/aip/journal/pof2/25/7/10.1063/1.4812285
2013-07-25
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Stability of steady gravity waves generated by a moving localised pressure disturbance in water of finite depth
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/7/10.1063/1.4812285
10.1063/1.4812285
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