Calculation of Wave Forces Using Morrison's Equation Under Small Amplitude Wave (Linear Wave) Theory

Morrison's Equation serves as a fundamental wave force calculation formula based on small amplitude wave (linear wave) theory, widely applied in wave mechanics courses within naval architecture and ocean engineering disciplines. The equation primarily computes wave-induced effects on marine structures, including wave forces and wave moments. Wave forces represent the hydrodynamic loads exerted by waves on submerged or floating bodies, while wave moments refer to the rotational effects caused by wave action. From an implementation perspective, Morrison's Equation typically requires numerical integration methods where: - Wave kinematics (particle velocities and accelerations) are calculated using linear wave theory functions - Force components are separated into drag and inertia terms using empirical coefficients - Time-domain simulations often employ discretization schemes for structural elements The equation finds extensive applications in analyzing wave impacts on offshore structures such as wind turbines, platforms, and ship hulls. Key computational considerations include: - Proper selection of hydrodynamic coefficients (Cd and Cm) based on structure geometry - Handling of relative velocity calculations between fluid and structure - Implementation of frequency-domain or time-domain solution approaches As a critical theoretical tool in naval architecture and ocean engineering, Morrison's Equation offers robust methodology for wave load predictions with significant practical applications in offshore industry design and analysis.