Advances in mathematical modelling to study complex sound propagation in an inhomogeneous moving ocean: Unlocking the Operational Advantage of the Oce

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The Ocean is a vast, complex and dynamic environment that is continuously evolving. Modellingthe propagation of sound through the ocean is a multi-faceted and extremely challengingproblem. There are a plethora of non-trivial time-dependent phenomena that affect the propagationof 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 equationvia 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 themathematical 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 [?], andparabolic 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 andhigh 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 alsoused 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 switchefficiently between solving techniques as the environment and specific challenges demand (includingoperational or computational requirements). The majority of the numerical solutionslisted 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 andapproximations applied. For example, low and medium-range frequency scattering and reverberationfrom the ocean boundaries are not presently included in stratified layer models suchas NM and wavenumber integration methods. Similarly, PE techniques cannot easily treatbackscattering, being based on a reduced form of the wave equation. This project seeks toaddress those issues by studying the dynamic and scattering effects, which are highly relevantfor low-frequency sonar modelling, as well as for range and depth-dependent sound propagationat all frequencies for defence and security applications.