Add FFT wave generation using ECKV variance spectrum with cos-2S spreading function

[srmainwaring]

This issue is to track improvements to the FFT wave generation model.

Issues with the current FFT wave model:

• There are missing scale factors when discretising the continuous Pierson-Moskowitz (PM) variance spectrum which means the simulated spectrum is not correct (and does not behave at all well as the resolution N is altered).
• The PM spectrum is omni-directional and the method used to implement travelling time-dependent waves is not very natural (and possibly is not Hermitian in the frequency domain leading to an imaginary component in the wave field).
• It is not possible to set the wave direction from the parameters (or rather it is, but it has no effect).

Proposed solution:

• Follow Curtis Mobley's detailed tutorial on generating sea surfaces from Ocean Optics taking care to include the correct scaling when transitioning from continuous one-sided spectra to discrete two-sided spectra
• Use the ECKV omni-directional spectra with the cos-2S spreading function to generate travelling time-dependent waves
• Allow the downwind direction to be specified as a parameter (using an angle from the positive x-axis (east in ENU coordinates))
• Add checks for various statistical properties of the waves and confirm the Fourier amplitudes are Hermitian.

Tracking implementation on this branch:

• https://github.com/srmainwaring/asv_wave_sim/tree/feature/fft-eckv-cos2s

Task list

• [x] Add new FFT wave simulation class
• [x] Integrate FFT class into OceanTile and enable in SDF models
• [x] Add ECKV omni-directional spectrum
• [x] Add ECKV and cosine-2S spreading functions
• [x] Port prototype from Python to C++
• [x] Check FFTW vs NumPy / SciPy FFT conventions
• [x] FFT for wave height
• [x] Enable parameters to control wind speed and direction
• [x] FFT for wave height derivatives
• [x] FFT for horizontal displacements
• [x] FFT for horizontal displacements derivatives
• [x] Update SDF parameter options
• [x] First round of optimisation

[srmainwaring]

Waves for u10 = 7 m/s with downwind rotated clockwise 45 deg from the positive x-axis

Issues

Models appear to 'bounce' on the waves - could be:

• Wave speed is too high - check spreading function and dispersion
• Update rate of 30 Hz for wave physics is too slow - try increasing
• Water patch is too coarse - try refining and migrate the markers for the patch and water levels for debugging

=> Resolved: issue was error in dispersion calculation loop (wrong k-vector ordering). Fixed in https://github.com/srmainwaring/asv_wave_sim/commit/5ff2abc83856ac2e31fa1d29ec361c6f44fa6924

[srmainwaring]

Closed by #23