The velocity potentials of a point source moving at a constant velocity in the upper layer of a two-layer fluid are obtained in a form amenable to numerical integration. Each fluid layer is of finite depth, and the density difference between the two layers is not necessarily small. The far-field asymptotic behavior of the surface waves and internal waves are also derived using the method of stationary phase. They show that the wave system at the free surface or at the interface each contains contributions from two different modes: a surface-wave mode and an internal-wave mode. When the density difference between the two layers is small or the depth of the upper layer is large, the surface-wave mode mainly affects the surface waves while the internal-wave mode mainly affects the internal waves. However, for large density difference, both modes contribute to the surface wave or internal wave system. For each mode, both divergent and transverse waves are present if the total depth Froude number is less than a certain critical Froude number which is mode-dependent. For depth Froude number greater than the critical Froude number, only divergent waves exist for that mode. This classification is similar to that of a uniform fluid of finite depth, where the critical Froude number is simply unity. The surface waves and internal waves are also calculated using the full expressions of the source potentials. They further confirm and illustrate the features observed in the asymptotic analysis.
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