%ABorcea, L%AGarnier, J%ASolna, K.%Anull Ed.%BJournal Name: Proceedings of the Royal Society of London; Journal Volume: 477
%D2021%I
%JJournal Name: Proceedings of the Royal Society of London; Journal Volume: 477
%K
%MOSTI ID: 10281522
%PMedium: X
%TOnset of energy equipartition among surface and body waves
%XWe derive a radiative transfer equation that accounts
for coupling from surface waves to body waves and
the other way around. The model is the acoustic
wave equation in a two-dimensional waveguide
with reflecting boundary. The waveguide has a thin,
weakly randomly heterogeneous layer near the top
surface, and a thick homogeneous layer beneath it.
There are two types of modes that propagate along the
axis of the waveguide: those that are almost trapped
in the thin layer, and thus model surface waves,
and those that penetrate deep in the waveguide,
and thus model body waves. The remaining modes
are evanescent waves. We introduce a mathematical
theory of mode coupling induced by scattering in the
thin layer, and derive a radiative transfer equation
which quantifies the mean mode power exchange.We
study the solution of this equation in the asymptotic
limit of infinite width of the waveguide. The main
result is a quantification of the rate of convergence of
the mean mode powers toward equipartition.
%0Journal Article