Questions about the scope of nonlinear application

[Qiujue Jiang]

Dear FUNWAVE-TVD community.
I know that in the derivation of the control equations of FUNWAVE-TVD, O(μ^2) and all the ε terms in this premise are preserved, so it is fully nonlinear Boussinesq equation model.
I need to simulate a strong nonlinear wave condition with water depth d = 1.73m, period T = 8s, wave height H = 0.83m, μ=kh=0.34, ε=A/d=0.24, and according to the wave theory applicability range in The Shore Protection Manual, this condition has d/gT^2 = 0.0028 H/gT^2 = 0.0013, which is in the range of Cnoidal wave. The results of my simulations are shown below, using a grid scale of 80 grids per wavelength and a fixed time step that satisfies the CFL law. The simulation results show that the shape of the wave is quite different from the Cnoidal wave, so I would like to ask whether FUNWAVE-TVD is suitable for simulating waves in the Cnoidal wave range and whether there is a wavemaker suitable for simulating such waves. And when I checked the related literature, I found that most of the waves simulated with FUNWAVE-TVD are in the stokes wave range.
Thanks!
Jiang Qiujue 2023/06/22

[Kirby, James T]

Jiang,

The cnoidal wave is a periodic solution of equations (Boussinesq or KdV) falling in the weakly dispersive regime, which Funwave is a member of, so its use for this case is totally appropriate.  It would be the Stokes wave regime that would be a stretch, as this range extends to deep water, while the range of validity of Funwave does not.

Jim Kirby

p.s. I don't see anything in particular wrong with your plotted results.  Note that the internal wavemaker is linear - you aren't going to get a steady wave at large amplitude since there is going to be an immense amount of energy exchange between Fourier modes, hence the spacial beating effect in your figure.

If you want to try to get a cleaner large amplitude wave, you are going to have to use the option of specifying eta and u at the domain boundary.

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Jim Kirby
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[Qiujue Jiang]

Thank you for your response.

I would like to ask which wavemaker I need to use if I want to specify eta, u and v at the left (west) boundary, it looks like wavemaker = LEFT_BC_IRR or INI_OTH, and the hotstart option won't do the job.

[Qiujue Jiang]

And about wavemaker = ABS, I found from the source code that this wavemaker seems to have a wave absorbing ability (because the R_sponge_wavemaker and A_sponge_wavemaker need to be specified).

But I didn't find any description about it, is this wavemaker available at the moment (I'm using FUNWAVE-TVD version 3.6)?

[fyshi...@gmail.com]

The absorbing and generating boundary condition is a newly developed option. A brief documentation can be found at

https://fengyanshi.github.io/build/html/tide_module.html

see 'Combined tidal and absorbing-generating boundary condition'.  A simple test case is in /tide_gen_abs_data/ in the FUNWAVE-TVD package (github master branch). 

[Qiujue Jiang]

Thank you for your reply！