Low Froude number potential energy resonances in uniform stratification

Internal wave effects generated by a solid body moving uniformly at constant depth through a density-stratified fluid of uniform depth are investigated. In particular an averaged potential energy Γ per unit track length is defined and analyzed under the assumptions of linear theory, uniform stratification, and rigid lid boundary conditions. A general expression is found for Γ in terms of the intrinsic causal structure of the fluid system and the geometric properties of the generating object. It is found that, as the speed of the body decreases to zero, Γ passes through an infinite sequence of infinite-amplitude resonances. A source function approximation is used to model the shape of the generating object and numerical evaluations are made for the case of a sphere. A consideration of the infinite-depth limit allows one to see Γ in terms of the resonance-inducing effects of the rigid lid boundary conditions in conjunction with the relatively smooth and finite “background resonances” associated with pure buoyancy effects.