Ship waves in a stratified ocean

The velocity potential for a simple source moving in a straight line at constant depth in a two-layer ocean is obtained by the Fourier transform method. It is used to develop a formula for the wave-making resistance of a ‘thin’ ship for both surface and internal waves. An asymptotic expansion is used to delineate quantitatively the internal wave system. It is shown that at speeds less than the critical speed transverse and divergent wave systems are excited, while at speeds greater than the critical internal wave speed only the divergent wave system is excited. Examples of the shape of wave crests and of wave heights are given.