Svaerd-Kalisch model

[pnavaro]

The implemented Svaerd-Kalisch model differs from the model in the published paper (JCP - equations 11-12). This model has 3 parameters, and when α or γ are non-zero, it is not suitable for modeling water wave propagation. This can be observed by noting that the phase velocity is not an even function of the wave number. As a side note, the convention for computing this quantity for negative wave numbers is not consistent across all models (Euler and Svaerd-Kalisch models are opposite to all other models). We suggest adding a note in the documentation to clearly indicate the parameter restrictions and warn users about the configurations that are not appropriate.

using DispersiveShallowWater
using Plots

eta0 = 0.0
reference_height() = 0.8
h0 = reference_height()
g = 9.81
disp_rel = LinearDispersionRelation(h0)
k = -5.0:0.01:5.0

bbm = BBMEquation1D(; gravity = g, eta0 = eta0, D = h0)
c_bbm = wave_speed.(disp_rel, bbm, k; normalize = true)
plot(k, c_bbm, label = "BBM")

sk = SvaerdKalischEquations1D(; gravity = g, eta0 = eta0,
                              alpha = 0.0, beta = 0.2308939393939394, gamma = 0.04034343434343434)
c_sk = wave_speed.(disp_rel, sk, k; normalize = true)
plot!(k, abs.(c_sk), label = "Svärd-Kalisch")

JOSS review #9361

[JoshuaLampert]

Good catch! Yes, it is true that the Svärd-Kalisch model has some unphysical properties in the $\alpha$ and/or $\gamma\neq 0$ case, which we also briefly discuss in our paper: https://link.springer.com/article/10.1007/s44207-025-00006-3. The currently implemented model is the one from the preprint of Svärd and Kalisch. We already developed and implemented a discretization for this model before their article was published in JCP. We decided to keep the version including the $\alpha$ and $\gamma$ because it is mathematically a true generalization of the JCP version (which just corresponds to a specific parameter choice) and from a mathematical/numerical standpoint (we are mathematicians working on numerical methods) the more general model is still interesting. I created #262 to clarify this in the docstring.