Cnoidal

Table of Contents

• Properties
• Model equations
• Default model coefficients
• Usage
• Further information

Note

Under construction - please check again later

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:

• $FOAM_TUTORIALS/multiphase/interFoam/laminar/waves/cnoidal

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