emd.simulate.abreu2010#

emd.simulate.abreu2010(f, nonlin_deg, nonlin_phi, sample_rate, seconds)[source]#

Simulate a non-linear waveform using equation 7 in [1].

Parameters:

ffloat: Fundamental frequency of generated signal
nonlin_degfloat: Degree of non-linearity in generated signal
nonlin_phifloat: Skew in non-linearity of generated signal
sample_ratefloat: The sampling frequency of the generated signal
secondsfloat: The number of seconds of data to generate

Returns:

ndarray: Simulated signal containing non-linear wave

Notes

This function implements equation 7 in [1].

$u(t) = U_wf \frac{ sin(\omega t) + \frac{r sin \phi}{1+\sqrt{1-r^2}} } {1-r cos(\omega t+ \phi)}$

Where $\phi$ is nonlin_phi - a waveform parameter $(-\pi/2 \leq \phi \leq \pi/2)$ related to the biphase and $r$ is nonlin_deg - an index of skewness or nonlinearity $(-1 \leq r \leq 1)$ .

This equation is a generalisation of equation 14 in [2]. This paper highlights 3 cases for $\phi$ .

$\phi = 0$ , resulting in an accelerated skewed wave (sawtooth wave profile);
$\phi = - \pi/2$ , a velocity-skewed wave (with a velocity shape similar to a 1st-order cnoidal wave);
$\phi = - \pi/4$ , corresponding to a wave with both velocity and acceleration skewnesses

References

[1] (1,2)

Abreu, T., Silva, P. A., Sancho, F., & Temperville, A. (2010). Analytical approximate wave form for asymmetric waves. Coastal Engineering, 57(7), 656-667. https://doi.org/10.1016/j.coastaleng.2010.02.005

[2]

Drake, T. G., & Calantoni, J. (2001). Discrete particle model for sheet flow sediment transport in the nearshore. In Journal of Geophysical Research: Oceans (Vol. 106, Issue C9, pp. 19859-19868). American Geophysical Union (AGU). https://doi.org/10.1029/2000jc000611