Remote stationary wave field generated by local perturbing sources in a flow of stratified fluid (Q1093484)

A linear formulation is used to study the problem of stationary waves formed in a uniform flow of an inviscid incompressible vertically stratified fluid past a point source or a mass dipole. Formulas are derived representing the characteristics of the wave field in the form of the sum of single integrals. A method is developed for constructing complete asymptotic expansions of the integrals obtained for large distances from the wave generator, including uniform expansions near the leading fronts of the separate modes. Approximate solutions of the problem in question exist. In the case of a deep liquid the asymptotic form uniform in the neighbourhood of the leading fronts is expressed in terms of Fresnel integrals, and in the case of a liquid of finite depth by Airy functions.