Properties

Solitary wave

Model equations

The wave height is modelled by the equation:

\[ \eta = 1 + \epsilon s^2 + \frac{3}{4} \epsilon^2 s^2 t^2 + \epsilon^3 \left( \frac{5}{8} s^2 t^2 - \frac{101}{80} s^4 t^2\right) \]

and

\[ \epsilon = \frac{a}{h}; s = \mathrm{sech} (\alpha x); t = \tanh(\alpha x); \alpha = \sqrt{\frac{3}{4} \epsilon} \left( 1 - \frac{5}{8} \epsilon + \frac{71}{128}\epsilon^2 \right) \]

where:

$ h $	=	water depth
$ a $	=	wave amplitude
$ t $	=	time

Default model coefficients

Usage

Inlet patch example

<patch>
{
    alpha           alpha.water;
    waveModel       Grimshaw;
    nPaddle         1;
    waveHeight      0.05;
    waveAngle       0.0;
    activeAbsorption no;
}