Internal waves generated by a horizontally moving source

Abstract The internal waves produced by either a moving body or the collapsing wake behind a moving body in a stratified fluid are calculated asymptotically (at large distances behind the source) on the hypotheses of small disturbances, the Boussinesq approximation, and the slender-body approximation (the transverse dimensions of the body and wake are small compared with the wavelengths of the significant internal waves). Explicit results are given for two, complementary models: (a) a constant-N model, in which the density gradient is constant and (b) a thin-thermocline model, in which the density gradient peaks sharply in a thin layer and is elsewhere negligible. The internal-wave spectrum is continuous in (a) and discrete in (b); however, only the dominant mode is included in the explicit results given for (b). A WKB solution also is given for a thermocline model. This approximation does not give an adequate representation of the dominant mode but does provide estimates of the contributions of the higher modes that are neglected in the thin-thermocline model. These contributions are typically negligible relative to that of the dominant mode in the neighbourhood of the maximum, free-surface disturbance.