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Water Wave Mechanics
Small-Amplitude Wave Theory
Small amplitude wave theory provides estimates of many of the basic engineering properties of the monochromatic wave train on a fixed water depth. The result is a progressive, monochromatic wave solution to the boundary value problem consisting of the governing equations of motion for irrotational motion of an inviscid fluid (Laplace's Equation) and the appropriate boundary conditions.
Engineering Properties
The solutions developed in Small-amplitude Wave Theory for standing and progressive water waves provide the basis for applications to numerous problems of engineering interest. For example, the water particle kinematics and the pressure field within the waves are directly related to the calculation of forces on bodies.
Group Velocity and Energy Flux
Group Velocity of wave is the speed at which energy is transmitted. Energy Flux is defined as the rate at which the energy is transferred. Energy Flux also is the function of Group Velocity.
Wave Forces
An important application of water wave mechanics is the determination of the forces induced by waves on fixed and compliant structures and the motions of floating objects. All objects, whether floating on the sea or attached to the bottom, are subjected to wave forces, and therefore these forces are of central interest to the designer of these structures.