Internal Wave Generation in Uniformly Stratified Fluids. 1 ... - LEGI

educes to the Green’s function. Now, if the initial state of the fluid is taken just before the
impulse, at t = 0 – , ψ 0 (r) = 0, ψ 1 (r) = 0, m(r, t) = δ(r) δ(t) and G(r, t) arises from the mass source
term in (B3). If, on the other hand, the initial state refers to t = 0 + , just after the impulse,
irrotational initial conditions are ψ 0 (r) = 0 and ψ 1 (r) = – 1/(4πr), while m(r, t) = 0; G(r, t) arises
now from the initial data term in (B3), by virtue of Δ (1/r) = – 4π δ(r). Thus, the equivalence of
both approaches is proved for the Green’s function. As any internal wave field may be built
by a superposition of elementary impulses, this conclusion is at the same time proved from a
general point of view.
Internal wave generation. 1. Green’s function 49