Enhanced Time-Series Water Wave Model through Refinement of Convective Acceleration and Driving Force in the Velocity Equation

This study investigates the simplest time series type of the Boussinesq equation, namely the Airy long wave model. The primary limitation of this model is its applicability only to short wave conditions with very small amplitudes, which are significantly smaller than the maximum wave amplitude permitted for a given wave period. The source of this limitation is identified as the treatment of convective acceleration in the water particle velocity equation. Model refinement is introduced by interpreting the convective acceleration as a hydrodynamic force whose positive direction extends from regions of higher kinetic energy toward regions of lower kinetic energy. This interpretation requires assigning a negative sign to the convective acceleration term. In addition, the hydrostatic force commonly employed corresponds to the surface hydrostatic force, whereas the velocity equation utilizes depth averaged velocity. To ensure consistency, this force must therefore be reformulated as the depth averaged hydrostatic force.