Linear surface capillary-gravity short-crested waves on a current

One of the forward situations in the study of water waves is the basic three-dimensional surface wave motion of short-crested waves. Capillary waves result in rich effects concerned closely with remote sensing in the open ocean. Ocean currents experience a complete process in surface wave motion. Based on the above ideas, a linear dynamical system of surface capillary-gravity short-crested waves is developed by considering the current effects, thus leading to the following analytical expressions of the kinematic and dynamic variables: the wave height, the wave steepness, the phase velocity, the wave-particle velocities, accelerations and trajectories and the wave pressure. A number of the classical, typical and latest special wave cases can arise from these expressions.