Broadband properties of potential and kinetic energies in an oceanic waveguide

The energetic properties of an acoustic field can be quantified through the potential (Ep) and kinetic (Ek) energies. This article derives broadband properties of Ep and Ek in an oceanic waveguide, with restriction to a far-field context under which the acoustic field can be described by a set of propagating trapped modes. Using a set of reasonable assumptions, it is analytically demonstrated that, when integrated over a wide enough frequency-band, Ep = Ek everywhere in the waveguide, except at four specific depths: z = 0 (sea surface), z = D (seafloor), z = zs (source depth), and z=D-zs (mirrored source depth). Several realistic simulations are also presented to show the relevance of the analytical derivation. It is notably illustrated that, when integrated over third-octave bands, Ep≃Ek within 1 dB everywhere in the far-field waveguide, except in the first few meters of the water column (on a dB scale, no significant difference is found between Ep and Ek for z = D, z = zs, and z=D-zs).