Waveform Diagrams of 2D and 3D Ocean Wave Simulation Program

Ocean wave simulation is a significant subject in marine engineering and computer graphics, where mathematical models can replicate the dynamic forms of waves. This MATLAB-developed program generates waveform diagrams for ocean waves in both 2D and 3D environments, providing a visualization tool for related research.

P-M Spectrum Calculation The core program bopu.m implements the standard P-M spectrum (Pierson-Moskowitz spectrum), a classic model describing ocean wave energy distribution. Users only need to input wind scale and frequency parameters to obtain the energy spectrum curve corresponding to specific wind conditions. The spectrum reflects how wave energy distributes across frequencies, forming the foundation for subsequent waveform generation. The algorithm calculates spectral energy density using wind-speed-dependent parameters to model fully developed sea states.

2D Waveform Generation The hailangboxing.m program constructs 2D ocean waves through linear superposition method. After inputting wind scale and frequency numbers, the program generates wave profiles for corresponding sea conditions based on the P-M spectrum. This method is suitable for scenarios requiring rapid analysis of wave profiles, such as coastline erosion studies. The implementation involves inverse Fourier transforms of spectral components with random phases to create time-evolving wave surfaces.

3D Waveform Extension erweihailangboxing.m extends the 2D foundation by introducing directional spectrum with additional angle parameters. By superimposing wave components from different propagation directions, the program ultimately outputs spatially three-dimensional dynamic sea surface effects. This simulation can be used for ship navigation simulation or offshore platform design. The code incorporates directional spreading functions to model wave energy distribution across different propagation angles.

Fractal Method Comparison SDwave.m employs fractal geometry methods to generate ocean waves, providing a technical contrast to the linear superposition approach. The fractal method constructs irregular waves through self-similarity principles, making it more suitable for representing nonlinear characteristics like breaking waves, demonstrating the diversity of wave simulation solutions. The algorithm uses fractional Brownian motion or similar fractal techniques to create realistic wave height variations.

This toolchain covers the entire process from spectrum calculation to spatial waveform rendering. Users can choose between simplified 2D analysis or immersive 3D simulation according to their needs. By adjusting wind scale parameters, users can also observe how waveforms change under different sea conditions. The modular design allows flexible parameter configuration for various research applications.