Cnoidal

Properties

• Regular waves

Model equations

The wave height is modelled by the equation:

$$\eta = H \left[ \frac{1}{m} \left( 1 - \frac{E(m)}{K(m)} \right) - 1 + cn^2\left( 2 K(m) \frac{x - ct}{\lambda} \right) \right]$$

Where:

$\lambda$ : wavelength

$m$ : elliptic parameter that depends on the wave characteristic

$K(m)$ : complete elliptic integral of the first kind

$E(m)$ : complete elliptic integral of the second kind

$cn$ : Jacobi's elliptic functions

$c$ : wave celerity

$H$ : wave height

$t$ : time

Default model coefficients

Usage

Inlet patch example

<patch>
{
    alpha           alpha.water;
    waveModel       cnoidal;
    nPaddle         1;
    waveHeight      0.1;
    waveAngle       0.0;
    rampTime        6.0;
    activeAbsorption yes;
    wavePeriod      4.0;
}

Further information

Source code:

• Foam::waveModels::cnoidal

References:

• ...

Tutorials:

• cnoidal