MATLAB Program for Ocean Waveform Generation with Spectral Analysis Implementation

Waveform generation for ocean waves is a crucial technique in marine engineering and hydrodynamics research. MATLAB serves as an ideal tool for implementing such simulations due to its powerful mathematical computation and visualization capabilities. Ocean waveforms are typically constructed by superimposing multiple cosine waves with different frequencies and amplitudes, with the core methodology based on spectral analysis from linear wave theory. The implementation process primarily consists of three key steps: First, determining the target wave spectrum (such as Pierson-Moskowitz or JONSWAP spectrum), which describes the distribution of wave energy across frequencies. In code implementation, this involves defining spectral density functions that calculate energy distribution based on input parameters like significant wave height and peak period. Second, generating random phase angles for each frequency component to ensure waveform non-repetitiveness, typically achieved using MATLAB's random number generation functions (e.g., rand or randn) multiplied by 2π. Finally, synthesizing all components into time-domain waveforms through inverse Fourier transform, implemented using MATLAB's ifft function for efficient computation. The program typically includes parameter adjustment modules that allow users to input characteristic values such as significant wave height and peak period to control waveform morphology. These parameters are processed through spectral calculation functions that automatically scale frequency components accordingly. In advanced applications, directional spectra may be incorporated to simulate three-dimensional sea surfaces, or nonlinear correction terms can be added to improve simulation accuracy under severe wave conditions. This waveform generation method is not only applicable for ship seakeeping tests but also provides input conditions for load calculations on offshore structures. Key MATLAB functions involved in implementation include: fft/ifft for Fourier transformations, spectrum generation functions for different wave models, random phase initialization using random number generators, and visualization tools like plot and surf for waveform analysis. The algorithm efficiently handles large numbers of frequency components through vectorized operations, making it suitable for real-time simulation scenarios.