PhD in Underwater Acoustics

“Advances in mathematical modelling to study complex sound propagation in an inhomogeneous moving ocean”

The aim of this well-funded PhD project is to develop models for underwater sound propagation through a moving inhomogeneous ocean, with an emphasis on enhancing the understanding of critical dynamic aspects, including:

  • Internal waves;
  • Microstructure variability;
  • Scattering by rough surfaces, both stationary (seabed) and moving (sea surface); high sea states bring additional dynamic challenges such as large waves and infusion of air bubbles;
  • Seasonal, diurnal, and inter-diurnal changes;
  • Slow-moving horizontal currents, fronts, and eddies.

There is a lack of clarity within current literature as to the optimal representation of these dynamic phenomena within models, even for simplified two-dimensional cases. This project will address that issue by providing new insights that will also facilitate the development of three-dimensional and full four-dimensional, time-dependent propagation models.

About the project

Sound propagates more efficiently than both light and radio waves in the ocean meaning that underwater acoustic wave propagation has been studied and utilized for a variety of applications, including sonar technologies; underwater communication, navigation and exploration; ocean acoustic tomography and climatology. Underwater acoustics is widely used by marine creatures and is central to human interaction with the ocean and its marine life. The propagation of sound in the sea is a highly complex process that depends on a wide range of factors that change both spatially and temporally, and at different scales. Even on the calmest days, the ocean is constantly moving, and affecting the way that sound propagates.

Only the simplest factors are included in existing propagation models and developing new models, that can be used to increase understanding of these factors, presents both independent and inter-dependent challenges.

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 is best suited to high frequency applications, whereas normal mode (NM) and parabolic equation (PE) models are better suited to low frequency applications. Direct discretization methods, such as finite element (FE) or finite difference (FD), are capable of solving full models but are computationally intensive.

The project will develop new adaptive hybrid models which are able to switch efficiently between solving techniques as the environment and specific challenges demand (including operational or computational requirements). These models will incorporate advances in FE methods, via GPU parallel computing capability that has been largely untapped for underwater acoustics, and hybrid coupling methods. New ways of representing dynamic ocean mechanisms will be developed, and environment-specific modelling tools and innovative mathematical representations will be implemented in each or a combination of the models. Some of the techniques that will be used include:

  • analytical scattering techniques such as stationary phase approximations of Kirchhoff approximation (small grazing angles) and perturbation (large grazing angles) theory for seabed and surface scattering phenomena;
  • solitary internal wave modelling; characteristics of internal waves for both shallow and deep water will be studied;
  • hybrid modelling methods that have been developed for obtaining acoustic color templates and for ultrasonic non-destructive testing;
  • localization phenomena associated with multiple reflections within an infinite waveguide that may be modelled using resonance theory;
  • machine learning for sufficiently large datasets.

Person specification

We are seeking a highly motivated candidate who should have, or expect to be awarded, a first-class or a master’s degree in Mathematics, Physics, Computer Science or a related area of science. Preferred skills include a strong mathematical background, a keen interest in programming, and excellent writing, communication, presentation and organization skills.

General information

The student will be based in the Department of Mathematical Sciences at the University of Liverpool and will have the opportunity to interact across different research communities including the National Oceanography Centre (NOC) and the University of Liverpool’s EPSRC Centre for Doctoral Training in Distributed Algorithms. The student will be supervised by Dr Stewart Haslinger and Dr Daniel Colquitt at the University of Liverpool and by Dr Duncan Williams at the Defence Science and Technology Laboratory. The project will include spending time at Dstl for a total of at least 3 months over the course of the 4-year PhD. The expected start date is September/October 2021.

To apply please click here and click the 'Apply online' button. Please quote Studentship Reference: MPPR001 in the Finance Section of the Application Form. For any enquiries, please contact Dr Stewart Haslinger on This email address is being protected from spambots. You need JavaScript enabled to view it.


Open to UK applicants

Funded studentship

A 4-year fully-funded EPSRC i-CASE studentship with the Defence Science and Technology Laboratory (Dstl) is available covering UK tuition fees, maintenance above the average UKRI Doctoral Stipend rate (up to £18,000 p.a. including a generous annual top up from Dstl, subject to contract) and an allowance for training, conference and research expenses. Due to the nature of the project, we are unfortunately only able to accept applications from UK applicants.

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