Evaluation and Optimization of Approximate Solutions for Water Wave Dispersion Equations Through Flume Testing

This study examines water wave dispersion relationships to provide accurate estimates of wave height and wavelength under real-world engineering conditions. It is essential for optimizing the design of port breakwaters, channel depths, and dock structures, ensuring they can withstand wave forces and improve long-term port stability. By enhancing the predictability of wave characteristics, the study contributes to more resilient and cost-effective marine infrastructure. The research compares theoretical models with flume test data, deriving simplified formulas for direct wave number determination and eliminating the need for iterative solutions. The results show that while theoretical models effectively describe the wavelength–frequency relationship for long wavelengths, nonlinear dispersion equations are required for smaller wave numbers. Eckart’s formula and the modified Fenton and McKee formula provide high accuracy (with a maximum relative error of about 0.3%) across all water depths. Logarithmic fitting improves accuracy in deep water (with a relative error of about 0.2%), while Nielsen’s optimized equations perform reliably in shallow water (with around 0.1% error). However, as wave number increases, Eckart’s formula shows significant deviations in shallow water, indicating the need for further refinement. The HUNT formula, the N-S formula, and the fourth-order equation offer superior accuracy (with a relative error of about 0.05%) and are recommended for solving nonlinear dispersion relationships. Of these, the fourth-order equation is particularly well suited for practical applications, providing precise results across varying water depths, while Taylor expansion solutions perform well only in shallow water.