We summarize the ray-theoretic description of Kelvin ship waves in deep and finite depth, deriving the relationship between wavevector and wake angle, the Kelvin wedge, and the scaling of amplitude along rays via wave action conservation, and we connect these to Froude numbers and interference effects between bow and stern waves.

We collect the ray-theoretic relations for wave patterns generated by a point source, derive the slope of characteristics and their connection to the group-velocity symbol \(G\), and clarify the geometric roles of wavefronts, wave vectors, and rays, culminating in a phase-distance relation \(\theta=k \cos \mu r\) for capillarygravity wakes.