Underwater acoustics: Modelling sound propagation in an inhomogeneous moving ocean

The Ocean is a vast, complex and dynamic environment that is continuously evolving. Modelling
the propagation of sound through the ocean is a multi-faceted and extremely challenging
problem. There are a plethora of non-trivial time-dependent phenomena that affect the propagation
of acoustic waves in an ocean environment, from environmental factors (e.g., temperature,
pressure, and salinity), to biological effects (interactions with animal and plant populations),
to anthropological effects (shipping, oil and gas extraction).
The propagation of sound in the ocean may be described mathematically using the wave equation
via appropriate choice of boundary conditions. There are five established solution techniques,
each of which has its limitations, such as range or frequency dependence, related to the
mathematical approximation applied, and computational burden. Ray theory, [1], [2] and [3],
is best suited to high frequency applications, whereas normal mode (NM), [4], [5] and [?], and
parabolic equation (PE) models,[6], [7] and [8], are better suited to low frequency applications
(in the description of these models, 1 kHz is considered a typical frequency to separate low and
high frequency regimes and applications extend from below a few Hz to several hundred kHz).
Direct discretisation methods, such as finite element (FE) or finite difference (FD), are also
used and are capable of solving the full wave equation but are computationally intensive.
The aim of this project is to develop new adaptive hybrid models that are able to switch
efficiently between solving techniques as the environment and specific challenges demand (including
operational or computational requirements). The majority of the numerical solutions
listed above may be efficient for the frequency and range dependence for which they are valid,
but this advantage in speed imposes a cost in fidelity through the various assumptions and
approximations applied. For example, low and medium-range frequency scattering and reverberation
from the ocean boundaries are not presently included in stratified layer models such
as NM and wavenumber integration methods. Similarly, PE techniques cannot easily treat
backscattering, being based on a reduced form of the wave equation. This project seeks to
address those issues by studying the dynamic and scattering effects, which are highly relevant
for low-frequency sonar modelling, as well as for range and depth-dependent sound propagation
at all frequencies for defence and security applications.