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

海洋是一个不断演变的巨大、复杂和动态的环境。对声音在海洋中的传播进行建模是一个多方面且极具挑战性的问题。从环境因素(如温度、压力和盐度)，到生物效应(与动植物种群的相互作用)，再到人类学效应(航运、石油和天然气开采)，海洋中的声波传播可以用波动方程通过适当选择边界条件从数学上描述。已有的求解技术有五种，每一种都有其局限性，例如与应用的数学近似有关的范围或频率相关性，以及计算负担。射线理论[1]、[2]和[3]最适合于高频应用，而简正模(NM)、[4]、[5]和[？]以及抛物线方程(PE)模型[6]、[7]和[8]更适合于低频应用(在这些模型的描述中，1 kHz被认为是分离低频和高频区域的典型频率，并且应用从几赫兹以下扩展到几百千赫)。这个项目的目的是开发新的自适应混合模型，能够在环境和特定挑战要求(包括操作或计算要求)之间有效地切换求解技术。上面列出的大多数数值解对于它们有效的频率和距离依赖关系可能是有效的，但这种速度优势通过应用各种假设和近似来施加保真度代价。例如，海洋边界的低、中程频率散射和混响目前不包括在NM和波数积分法等层状层模式中。同样，PE技术基于波动方程的简化形式，不能很容易地处理后向散射。该项目力求通过研究动态效应和散射效应来解决这些问题，这些效应与低频声纳模型以及国防和安全应用中所有频率上的随距离和深度变化的声音传播密切相关。

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.